My son has an extremely high arched palate, so bad that it took us and the drs a LONG time to rule out a cleft of the hard palate. Breastfeeding was a HUGE struggle, but we managed somehow.
Dr Brian Palmer is a dentist who has done some extensive research on it, you should google him and find his webpage. He has a slide show with some fascinating (but somewhat gorey because some pictures are cadavers) information about palate development.
Does your son show any signs of Pierre Robin Sequence? (link in my siggy) A cleft palate is NOT a necessary part of the sequence, just a recessed and small lower jaw that leads to the tongue placement being wrong in-utero which forms the hard palate wrong. Putting a name to it isn't necessarily helpful (as in, it doesn't mean there's suddenly a "cure") but it for some reason made me feel better, you know? And PRS is sometimes related to genetic syndromes, the signs of which might be very subtle, so it's worth reading about at least. My son's syndrome, for example, has such a huge range of clinical presentations, that sometimes it isn't diagnosed until much older (sometimes not even until you have a child more severely effected and the drs start testing family members...)
I had a somewhat narrow palate as a child and wore a palatal expander for a short time when I was 9 years old. It made a big difference! I never had any speech impairment, but did require serious orthdontics
I expect my son to need LOTS of orthodontics, too.
As for food...my son had major feeding issues. We discovered that puries were really difficult for him, he couldn't transfer them from the front of his mouth to the back. He also has severe dysphagia, so that contributed. Then we tried the softer solids, and that was a disaster, exactly what you described happened: they'd get all mushed up in his palate and get "stuck". We learned to do careful palatal sweeps after every meal because a few times I thought he was done eating and would put him down to play, and an hour later he'd be choking, and I'd find food that was presumably stuck in his palate that whole time. It got scary a few times.
He actually did better with foods that were a harder consistency, which meant he wasn't really on table foods consistently until well after his first birthday, and after he had enough teeth to be able to chew some. He has learned to compensate by NOT chewing, because if he chews too much, he loses his food. It freaks his speech therapists out a bit, they saw on a swallow study that he made no attempt to chew meat, and they panicked saying he was a high choking risk because of it. But if he does chew it, then he DOES choke.
We have altered some of his foods...for example, he can't eat regular bread, but does better if it's toasted. So even a PBJ is toasted for him. We are careful not to put too much peanut butter on the piece of toast, though, or it gets stuck. We have learned to let him choose how big of bites of food he takes (for example, we won't cut up a banana to give to him, we'll give him the whole banana so he can control how big the pieces are). We've had to learn to trust that his body will tell him what foods to eat, and how to eat them. It's scary, because I WANT to cut his grapes so he won't choke, but if do, they get stuck in the palate and he DOES choke. Catch 22 kind of.
I'd say that you should have him evaluated by a craniofacial specialist...find out if there's a cleft palate team at any of the hospitals near you, they can evaluate his palate very carefully to make sure that there isn't a hidden cleft, and there will be a feeding specialist on the team who will give you ideas on how to feed him.
Oh, something I forgot...my son does MUCH better with foods that are very strong flavored, spicey especially. It might be more because of his dysphagia, but he seems to be able to track food better in his mouth if it has a very strong flavor to it. He'll eat salsa with a spoon! I think that the flavor just makes him more aware of where the food is in his mouth. We add garlic and pepper to a lot of his foods, which seems odd for a two year old, but is really helpful.
Speech is a big problem for my son, but he also has hearing loss, dysphagia, oral hypotonia, a dysfunctional soft palate, an upper lip that has no movement, and likely a neurological issue (apraxia) that is all contributing to his lack of speech. It's hard to tell how much (if any) of his speech problems come from his hard palate shape.