We are doing a mini project in out tiny gardens this year, we have the lotties but this is an experiment for a project next year.We are all paved but for two tiny borders and we don'[t get a lot of sun in the front one, but I do have trees in huge pots, we have had cherries , peaches , pears and blueberries from them. The lack of light in the front made the 5 blueberries that were there about 2 weeks later than the 5 in the back. We also grew runner beans in the front in a huge pot with an obelisk in it, they were behind the lottie ones but they did quite well.
I would go for it, try to give toms and peppers the sunniest bit ,pick your varieties carefully and you can use big pots for them.
I would use the raised bed for other things.
This year will be a real test, so I will be interested to see how you get on.
By the way, I grow salad greens all year round in a small greenhouse and they do very well even without the good light that winter robs us of.
Good Luck
XX Jeannine