You have some good suggestions! I want to add that with my Aspy, now 13-yr-old, went through some speech therapy called "pragmatic speech". I learned so much taking him to the speech therapist - and participating in a lot of the sessions.
School is a place where there is regular schedules, routines, and expectations. Home is the place to relax - that simple difference might explain all the getting upset after school. You mention he is hungry - snack time needs to include some protein and happen before homework time. Even if my son doesn't have any homework to do, I turn that hour after the snack into reading time - it can be reading to me or reading to himself.
If you can find one, get an analog timer (it is like a clock countdown, sort of like the older style kitchen timer). The nice thing with this kind of timer is how the time remaining is visibly perceived - sounds unnecessary, but a digital timer becomes a distraction to my son because he is, practically, caught up in counting time along with the digital timer.
One suggestion I have is to watch your reactions to his actions. I have had to stop myself from saying "go to your room until you feel better" -- I now say, "go to your room (there is no restrictions on what he does in there) for 5 minutes, then you will come downstairs ready to do your homework". I'm always putting a time limit into my requests, my reprimands, everything.
I have also stopped asking "do you have any homework" but instead say "let me see your homework (completed stuff and assignments to be done)". In a way, this is making clear my expectations.
I needed to remind him what actions (behaviors) are appropriate and what is not, very often at first. Now, a couple of years later its a couple of times a month or so. I have even practiced with him: let's walk down the stairs with no stomping. Okay, once again. Great job! or have him purposely stomp down the stairs then to step normally down the stairs (I see that I have started defining what is "normal"). I talk about what I expect, what exactly it is that I want to see him do.
Find some way to compliment good behavior - at the minimum, acknowledge it! Being quiet when bad behavior happens, in a way, condones that behavior.
Don't forget to mention that this is a concern of yours to your child's psychiatrist (if you are only seeing a pediatrician, see if you can find a pediatric psychiatrist -- I think ours is invaluable to us).
Gosh, I think I could go on and on! Feel free to send me a private message, if you want.
Blessings!