My now 4 year old used to gag on the level 3 baby foods, she just didn't like the texture and I wonder if that's why your son "choked" on the mashed potatoes you made. Although my daughter never could swallow the level 3 baby food she had no problem what so ever with finger foods.
Just make sure the pieces are small, about the size of a pea to begin with and if you are really worried only give him one or two pieces at a time. Pea-size is too small to block his windpipe and if you make sure he swallows each one before he gets another than he can't choke on a mouthful of food. Hopefully, after a couple feedings like this you can feel more at ease with this transition.
Another thing I did was make sure I could eat whatever I gave my daughter without using my teeth. Sounds kind of silly, but I liked to test things out that way, figuring that if I could mash it with just my tongue than my daughter could certainly eat it with her gums and tongue :)
Some great things to try are avocados, and really soft cooked cubes of carrots. Keep the pieces small, control the amount your son gets and try to relax. He will be fine.