I got a bike fit recently. We started with cleats (moving them back a bit.) Next was the saddle, which went forward, up, and more level. Finally, the bars. Mine are narrow, which is perfect. The fitter wants me to rotate the levers higher, so I can get a more natural bend in the elbows while keeping the wrists neutral. Finally, I will go from a 110mm stem to 90mm. (It was between a 90 and 100, and I decided to get a 90 to really feel the difference. If it feels too cramped, 100 it is!)
Anyway, with my fitting process, the stem length was the final piece of the puzzle, not the first.
BTW, my stem is still on order. In the meantime, I’m riding with my hands back from the hoods. The cheapest and easiest way to try different positions is to fake it and position your hands where they would be with the new equipment. Easiest way to try before you buy.