You've already received such great insight/experience and I cannot really add anything there, but I do agree that I think your ped is jumping the gun a bit based on Isaac's age. I really think that with our early babies, some peds don't want/forget to look at their adjusted age for where they should be.
I'm sure all feeding therapists and peds differ on this, but ours always told us that Stage 3 foods were difficult for a lot of kids because the texture was so odd ... is it chewy or is it soft? For both of my kids, once they had the pureed stuff mastered (to the point they could handle it a bit thicker), I just started trying to find soft real food ... overcooked pasta and carrots come to mind.
And, for my sons, I took it as a sign that when they gagged on items, they just weren't ready for it. As long as you continue to offer Isaac opportunities to explore the new food, he will most likely get there.
I know for me, if I'm eating something that is supposed to be smoother (like mashed potatoes), I'm completely turned off if I get a bite that is lumpy.