I am not much help re: gardening in shade. Our summers here are hot enough that there has to be some shade on my raised beds or the crops won't grow.
Every area has its' own unique issues when gardening.
On intercropping, I have recently stumbled on two successes. One was interplanting my potatoes with bush beans. They were both very productive. The other is developing this winter. I plant my multiplier onions in October and they will grow through winter for a spring harvest. Well apparently last winters lettuce crop seeded freely in that raised bed. I have a nice stand of lettuce growing in among the onion plants. Neither one seems to protest sharing the space. I know you can't plant in winter but perhaps that type of intercropping might work for you in your planting season.
I had read an article on intercropping and plant compatibility. I will try to find it and link it here.
When you mentioned your lettuce crop being eaten by bugs, do you know what kind? If so, perhaps interplanting herbs or flowers to repel the bugs may be the answer.
Good luck with the new bed. Please stay in touch here.
