My concern would be that I know, from experience, that it is hard (sometimes effectively impossible) to reach through trellised/supported crops to get at other parts of the garden. I think you may have some difficulty reaching the back inside squares, although now that I notice your name, perhaps not ;)

but the onions together, radishes on the outside and move the position of the lettuces to be next to the onions for companion planting. They also do well near strawberries but since your strawberries are near your peas and beans and because onions are enemies of peas and beans I'd keep those as is.

Also in terms of companion planting, peppers like being near tomatoes and the tomatoes will help preserve the high humidity microclimate near the peppers to encourage larger fruits as well as balancing out their temperatures during days and nights so that they stay in their optimum blossom temps - both plants suffer from blossom drop if the temps go below 65(F) or above 90(F) while flowering.

Finally, for companion planting, a square or dedicated to marigolds in each bed and it will repel pests that attack your tomatoes, peppers and cucurbits (cucumbers, watermelons, cantaloupes, pumpkins, squash, etc.) They literally are the "wonder flower" for organic veggie gardening...just make sure to buy the "French Marigold" types as many of the newer cultivars don't produce the right chemical to make this happen. They're also pretty to look at... ;-p