Hi Jody,
I replaced my cockpit floor, stringers and teak 6 or so years ago and I hope the below narrative is helpful.
I believe what I did was use junky wood to make stringers that I could shave down easily until I had the right fit and height of the stringers fore and aft. There was a lot of putting boards in the boat and taking them out with marks on them to shave to the right fit. Was a bit tedious but worth it to get the right level and fit to the hull. Once I had the right shape to each stringer I cut the official stringer wood to match. I definitely remember screwing a few of the teak boards to the stringers in the garage and then placing the partially completed floor in the boat to check for fit again and even more shaping of the stringers. So if you are able to get the right fit with the stringers before hand it saves a bunch of time and labor later. Once I was happy with the fit and height it was easier to go into production mode in the garage and screw the rest of the boards to the stringers. I screwed on all the boards in the garage and then unscrewed and removed the outer boards so that I could glass in the ends of the stringers to the hull. Once the glass had set i re screwed in the outer boards.
I did place triangular supports under the port and starboard sides of the 2nd and 3rd stringers from the front and glassed them to the hull as well as placed a heavy duty stainless steel corner bracket under the forward stringer and through bolted to the center of the horizontal bulkhead board (the board before you step into the cabin). Those supports stabilized the floor wonderfully and made it very solid. I left the 2nd stringer from the front intact from side to side. I know many boats cut these off where the floor hatch is to make for easier access. I left mine in for support which I recommend.
Good Luck with your project - its a great one for the winter months and super satisfying once done for the spring.
Robin Durrschmidt
Ensign #363, Magic
Go Ensign Sailing!