I would imagine that if you take a U channel, invert it, and tab it onto a well prepared floor (all paint etc. ground off) then you would not need any screws. Screws have the disadvantage that they disturb the existing laminate and that they are potential stress points.
You've used your special method to force the keel back into alignment. If it retains the new shape or if you can make it retain the old shape while the new fiberglass cures (I assume you'd use epoxy) then you don't need any temporary fasteners.
I would make the stringer hollow (with 3/4" holes in a few places to allow water to drain freely) and I would aim for a having it at least as tall as its wide, as the height is what gives it the strength.
For aesthetic reasons, matching it to the keelson that's in front of the CB would be an obvious choice. That one is about as wide as the CB. As you go aft, you could reduce the height of the stringer (letting it gradually disappear into the floor, so to speak). That's what I'd do in my boat, because there's a drain plug in the bottom center of the transom.
It should be possible to pre-fabricate a bit of channel, then grind the edges for a tight fit, fair the corner where the edges meet the floor into a gentle curve by adding fairing compound and finally glass it onto the floor. With that approach, you could use a few dabs of 5 minute epoxy to "fix" the stringer in place.
If you build the stringer in place you need some kind of form, and unless you make a hollow form out of epoxy saturated cardboard, you're going to end up with a filled stringer - that always has the disadvantage of providing a secret place where hidden water can accumulate unseen.
I'm probably just writing down all the things you have thought of already
