Lumpy Foods

Help! My little one is having a hard time moving away from purées. We have been thickening his food with baby cereal and he does ok with that, but anything with any type of lumps he just gags and spits it out. I’m sure it is partly my fault as I tend to be a little paranoid about him choking and should have started him with more lumpy foods earlier, but I can’t go back and change that, so what have you all done to transition to more lumpy foods? Thanks!