I agree that 300 sq ft is too small to rotate crops to avoid pests. It is probably NOT too small to rotate crops to renew soil nutrients, however.
What you could do is grow larger amounts of fewer crops, and switch each year. For example, if you only grow potatoes every 3 or 4 years, it is much less likely that you will encounter beetle problems. Then again, if you neighbour is a potato farmer you will probably have to live with the beetles, regardless.
Otherwise, you could look at companion planting to reduce the numbers of pests. I have heard (but have not yet tried, although I've been meaning to) that planting flax with potatoes drastically reduces the number of potatoe beetles. It has something to do with the colour matching of flax flowers to potatoe flowers, which confuses the little bug(ger)s.
Yet another potato trick is to fall plant them so they get a really early spring start and can be harvested before the beetles gather steam. Alternatively, you can late start them (after the beetle season) and harvest late. I have had good luck with late starts, but not with early starts.
Lastly, there are many natural "pesticides" that you can try without going for the nasty chemicals: many people swear by spraying with a solution of tobacco-infused water (and tobacco plants are very easy to grow yourself).
And finally, a disclaimer: I live in Northern Ontario (about a zone 3b for gardening) and some of my timing strategies rely heavily on seasonal frosts and insect emergence which might not be at all similar to yours.