It sounds like you’re doing the right thing by imitating chewing to him -- but those little ones sure are smart, aren’t they?!

My son had some swallowing issues because he was born so prematurely, so I really feel for you on this issue. We were almost hyper-vigilant when he started eating soft solids because we were worried about him choking -- and I saw, when I changed his diaper, that some of his food (especially carrot chunks) went through whole.
I, too, thought that was hard on his digestive system and counterproductive if his body wasn’t able to absorb many nutrients from the food because his system couldn’t break it down. (My training as a CMT involved some study of the digestive system, so PM me if you want to talk about that more in-depth.)
So, I decided to buy a food mill -- and it was one of the best investments I made. I’m giving you a widget to the Kid Co. Food Mill (think I bought mine from the
One Step Ahead catalog) because it’s what we used and we were very pleased with the product.
What I especially liked about this food mill (aside from the fact that it’s portable and easy to clean) is that it grinds the food -- even things like meat -- into smaller bits, but there is still some texture to it.
Once my son started tasting food we had put through the mill, he pretty much gave up on any type of jarred baby food. And it worked out okay, because I could feed him a lot of the same things we were eating (less food prep) by just putting it through the mill.
So I would encourage you to do both -- keep working with him on chewing his food, but also put some through a food mill and offer that to him. Make sure to cut the soft foods that you’re trying to get him to chew into smaller bites so he can digest/absorb more; but, with the food mill, don’t puree things too much or he won’t learn the feel of a different texture.
Keep your mealtime fun and low-key and don’t worry about it if it takes him a little while to master -- he will get it eventually!