All of the comments and questions of our fellow members collectively reflect my own thinking on why your dough didn't brown up more.
Fro my experience, a dough may not brown up sufficiently for mainly three reasons. The first is that the dough is an immature same-day dough that has not been allowed to ferment long enough--typically only a couple of hours or so. The second is that the dough has overfermented to the point where all or most of the natural sugar in the flour has been used up by the yeast and there is too little left to caramelize and provide good coloration. The third is insufficient oven temperature or other baking-related problems, such as those mentioned by Cheesy.
If the problem wasn't oven related, then it is quite possible that your dough overfermented or was close to overfermenting. I think the amount of preferment (starter) you used (I estimate about 13-15% by weight of flour if your starter is like mine) was OK, even in a somewhat dormant state, but when you used warm water to compensate for the cool starter, you may well have accelerated the rate of fermentation of the dough such that, along with a total of 9 1/2 hours of room temperature fermentation, you pushed the dough past its optimum fermentation period. I asked you about your room temperature because if it was higher than normal (as is now occurring where I am in Texas), then that would also accelerate the rate of fermentation.
When I experience a slowed rate of browning, I do as Cheesy and DKM recommend and use the broiler element and try not to open and close the oven door too much since each opening of the oven door can lower the oven temperature quite a bit (the stone will still be hot, however). In your case, it sounds like the bake temperature was OK (since you noted your concern that the cheese would overcook), so I think you may want to try the broiler approach when you next experience insufficient browning. You might also want to try reducing the total fermentation time and/or use cooler water and less starter.
FYI, Teresa, I have been experimenting with a same-day, Lehmann NY style dough that I think will interest you. It uses a natural preferment and a room-temperature rise, a high hydration level (around 63%), can be made starting in the morning (e.g., before leaving for work) and finished about 9-10 hours later (e.g., upon return from work) and requires no handling of the dough whatsoever during the entire time of fermentation, requires no autolyse or other form of rest period, and yields an open and airy crust and a crust flavor that is equal to or better than a 24-hour retarded (refrigerated) Lehmann dough. Everything is lined up up the night before, including readying the starter the night before so that it is ready to roll the next morning. I haven't reported on the results of the experiment thus far, even though I think I succeeded in meeting every objective, since I want to fine tune the recipe and technique before posting it (at the Lehmann thread). However, I did take a photo of a couple of slices, and have presented the photo below.