It's a little hard to suggest without knowing how he handles the chunky baby food (step 3 meals with meat I think). Does he like that? I had made my own food, so I just gradually made it less & less soupy until it was just what we ate. What are his favorite baby foods? If applesauce for example, then have you tried small chunks of dried apples? If cherries or peaches, then have you tried yogurt with small pieces of the fruit in it? Cooked peas and carrot chunks are usually fairly soft foods that the consistency isn't too far off from baby food. Small pieces of pasta can be good texture too.
My eldest had reflux as a babe, the meds never did much, but we controlled it by changing formulas. She was better on soy when she was doing just formula, but the reflux started back up again when she started solids. This was fixed simply by switching her back to milk formula. She outgrew the reflux as she started eating people food. I know others aren't so lucky, but you may need to get that looked at more, and maybe speak with a nutrionist to help with food choice ideas that might help.
I had the opposite problem with my youngest, she hated baby food & went straight from the bottle to solids. I started mixing small portions of yogurt or aplesauce with her food, gradually putting more sauce than food until now she will eat applesauce and yogurt which had been unheard of for her. Could you try the opposite?
How has he done with the large teething biscuits or toast? They can be messy, but some kids do better eating solids after getting used to those first.
I have alway heard just to introduce healthy foods to babies/toddlers at every meal, eat well yourself, and they will pick up good habits and variety soon enough. I recall my nephew as a babe eating only graham crackers...nothing else - for days! He's 9 now and eats a good variety of foods.
I guess too, maybe your son is just not ready yet. There is no precise timeline when they have to start eating solids, just when they are ready. Just like walking; some at 9 months, some at 16 months. Some kids lose their first tooth at 4, some not until they're 6 or 7. It should be okay to let him start solids when he is ready.