A.F.
I wouldn't rush him to get started on finger-foods. He'll do it when he's ready. My son also gagged when I tried to give him stage 3 foods, but within a couple of weeks, he loved them. The first finger foods he did eat were the fruit puffs, cheerios, and bananas.
Also, keep in mind that they will gag when trying new things - they're just learning how the whole process works.
Good luck!