it would be really good to know which specific insects you are having trouble with...
to me it takes much more effort to till than to use a shovel to turn over a garden (i don't dig up an entire garden that often - my normal routine disturbs about 5-10% of a garden when i'm burying garden debris at the end of the season - i may surface scrape the whole thing but i'm only skimming the surface and in the harder clay areas i'm just cutting off weeds at the surface). tilling also may not really bury the bugs/stuff but spread it out through the whole soil layer being tilled, so if you are trying to get rid of things by burying, well it may not actually accomplish that.
that all said, if you are going to till the sooner the better IMO as that gives any of your mulch and buried stuff time to break down and for the soil community to sort itself out again.
the vegetable gardens i keep here are mostly left bare soil during the winter months. not because i think that is a good idea, but because Mom thinks this is how it has to be to look tidy. to me it looks sick. i want cover crops, i want to leave plant debris and mulches on top of the soil as it will protect from the wind and the rains and ...
if you can get it tilled quickly enough and get it planted with winter wheat or winter rye (the grain not the grass) it might get a chance to grow some before spring. then turn it under several weeks before your spring planting has to happen.
my own vegetable gardens have a few bugs here or there that i don't particularly like, but they are not annoying me badly enough i care to do much about them. i hand pick Japanese beetles here or there, but i'll never get them all.
i also don't think it a good idea to use pesticides or other biocides including many that people say are ok for organic crops. well, no, i like the various creatures i have around so i don't want to put something out in the gardens that might harm some of them that i care about. i'm willing to do things selectively and very targetted (manual removal only) or just change what i grow if i have to.
i also have areas in the gardens which are spaces used to protect the beneficial bugs during the off season since i have no cover on many gardens for the winter. as of yet i do not have aphid problems. i don't have too many other problems with too many bugs either. squash borers and squash bugs, yep, we got those, i try to grow resistant enough types and rotate plantings to different areas when the populations get to be too high.