Good luck with food trialing! My 3-year-old son has FPIES (no luck with growing out of it yet- we just failed a retrial). He also ate a ton of avocado when he was younger (it is still a safe food for us).
Squash is a common trigger- but since your son already passed sweet potatoes and peas (also common triggers)- he may be fine. Not listed on every site- but bananas are also a common trigger according to our dietician (I found that out after my son had a severe reaction). But, every kiddo with FPIES is different . . . you have to trial . . .
With rice being a trigger, I suggest treading very carefully with the other grains. Quinoa is often a safe food for kiddos with FPIES to grains. My son likes the Quinoa Queen cheerios (available online). This site also has good quinoa recipes: http://cradlerockingmama.com/recipes/ My son likes the quinoa drops on that site.
I would watch out for "soft" symptoms (like diaherra) as well as severe. It is quite the myth that every food a FPIES kiddo reacts to is automatically vomit to shock. (Not that that isn't real- we had that severe reaction as well.)
Even though we have our challenges, our son has always been at a healthy weight and has had good growth. Hope this information helps!