First of all I'm very improved by your work, because it shows your steps in an very straight forward way, that is in my opinion one of the best in science i have ever read (maybe except from a health effects study on coffee, which is in same aspects very similar) so I'm a little sad to write that i think that you made an failure and missed also to check an factor maybe because of some kind of prejudice or -, more likely - because it sounds to silly (similar to the version of English used in this text, where - except from this part - the use is not intentionally, only bad English, sorry) . The first point is the assumption of an constant(!) exponential development: the checks for many other correlations are so good that an interested reader like me can follow every of your test and the assuming an function known from biological developments is ... the first ten times reading very plausible and the data feedback is quite impressive so it's very understandable that this confirmation proves the assumption but .....
- what does it mean for the unknown influence? it would be an constant sink which taking every year 5% (numbers for decoration) from the population OR a constant changing in the environment that take every year more, but constant less more than the year before, from the same root conditions at the beginning of the season. A combination of two factors, one for the sink and one with direct impact change in opposite directions given the same amount, would be in theoretical also possible but would be to strange. So the assumption stated a fixed (resp. fixed changing) environment.
- thinking the assumption backwards, with no known change, we had 10-fold insects 35 years ago (possible of course, we have no data) and 25-fold 50 years ago (also possible, we have no data) but there has to be a maximum in the past, because a 625-fold in the mass of insects would very probably mentioned 1917. Thinking about a little bit longer time makes it very unlikely that an 27 years constant function is the 'real' match for the unknown function/correlation, even if the data gives us such pretty feedback.
- thinking backwards again in which time a probably maximum could be occurred and that maybe lower values before the maximum could exist, gives the idea that we have no baseline at all for all our calculation. In extreme we have reached nowadays a more 'natural' state than 25 years before (it's maybe hard to imagine, but we have really no data)

At this point i can't distinguish between other sources and the way with the maximum projection, because both gives the idea to the other, so thinking a maximum in the near past around 1985-1980 and at least lower values before gives the glimpse of the idea that air-pollution, witch reaches a maximum in many values around 1985(?) can be a major contributor for the changing (similar to the hypothesis that stronger plants resulting from more nitrogen gives harder conditions for plant eating insects especially butterfly caterpillar, that seems to be falsified with your data, but maybe only for the majority of the species in your study).

So an cite from the summary (PHYSIOLOGY AND MAINTENANCE – Vol. V - Plant-Insect Interactions and Pollution - Jarmo Holopainen) gives the idea of an biological foundation:
"Insect outbreaks have been observed in the surroundings of polluted industrial areas and along highways. Species feeding plant phloem or species that mine or bore in living plant tissues have been more successful on pollutant-exposed plants than chewing insect herbivores. Phloem-feeding aphids are good indicators of pollutant stress on many plant species. SO2, oxides of nitrogen, fluorides, or mixtures of pollutants have often promoted aphid performance. SO2 exposures have shown that response curve of aphids is bell-shaped, with a peak at an air concentration of 100 nL L-1. On the other hand, observations of aphid performance on O3-exposed plants have given very confusing results. Depending on the duration and concentration of O3 exposure or the age of the exposed plants, aphid growth on the same plants can be decreased or increased compared with control plants grown in O3-free air."

So we have a suggestion that feeding plant phloem or species that mine or bore may get increased by SO2, NOx, O3 or some other pollutants and maybe some others because of more dead plants, fungi or bacteria on weaken plants. If there are measurements in the past that analyzed the species (i think this was the originate reason for the samplings) which can be group into different feeding classes this should show a change in the distribution of different feedings groups (also for other possible causes of change)

The next step is the problem to get an reliable indicator to prove the idea. As you show very nice in your work it is impossible to find an 'real' indicator by hand and computer can test thousands of permutations, but sometimes they catch ghosts. First idea for a check was data from Krefeld, because the organization stays there and because the station is classified as a background measurement station, witch should be an better indicator for the situation in the roughly protected areas. Thinking the oxidizing potential would be the most impact NO2 should have have a double Impact than 03 or NO and higher temperatures should rise the damages and ... long thinking, short Krefeld data: no temperature, many missing O3 Files and whole years without NO2. Additionally the station seems to be classified by a different definition of background than the imagined places in the study. Next try was the result of a search for a station with green surrounding on the map. So found Roth, witch also provide data for SO2. After trying some reasonable approaches, that missed because they don't want, i tried a brute-force with the mean over all squares of O3+3*SO2 hour-data for the months April to August (Factor 3 for SO2 to match an assumed constant exponentiation after experience with 10 and 5 that don*t match in this way) with simple use of the last value for missing ones.

So the month May and June seemed very similar to fig 2a and July and August if mixed together. In short: at this point it looks as sweet as the data test for the assumed function and data looks sometimes too good also some ghost are not so far away as the ghost thinking in such situations. Without a biomass model or a trust-able lawyer, it can also give a simple exponentiation function (with a baseline) as the suspicious assumption from the study, so the data resp. the idea, needs contact to the data instead of ghosts.

A model that calculates from the biomass at a given time and an adjusted plant-damage indicator, that includes the 'normal' - without damage - feed/grow rate for the insects, over the following days should give at least the same performance as an fixed exponentiation, simple because it have so much free/unknown parameters, even if reduced to O3/SO2 and the suggested bell characteristic. Threshold values, scales etc. would probably gives the chance to match. And finding one parameter to outperform the exponentiation after that might be no difficulty. So it will never get a prove from global data-set in this way. Derive O3 data for a given location would be quite impossible because of it's - from the view of an observer - very unstable locale and temporal 'behavior'. With a little chance it might be possible to get not completely unreliable data for SO2 for distinct locations till the mid 1990's, because it is little more stable in the atmosphere, so it might allow to test the general approach and some justifications. If one of the measurements took place near an air-measuring than many derivations might be possible

So what might be the results?
The general correlation with the global data, together with external biological explanations and surveillance should show that the air-pollution IS a factor, but maybe it can calculate from nearly zero to a nearly or - assuming matching with the not provable locale distribution- exactly 100% contribution to the formerly unknown causes.

So people who want to know the cause have the factor and people who are primarily interesting in the possible light contribution can make photos at night in the surroundings of the locations to prove if there might differences in the local constant sinks from the assumed constant exponentiation function.

A known factor in a random size might not much better than a fixed unknown, from some points of view, but maybe this is the more realistic one.

Maybe the data gives some fences or findings in distribution changes of different feeding classes shows them.