Yep.
[...] I currently have UltraFire Protected 14500 3.7v 900mAH batteries. Is there a battery that will run at a constant or steady voltage until it needs recharged, like the AW IMR 14500 3.7v 600mAH? [...]
There is no battery that I am aware of, including the IMR's, that have a flat discharge rate. That kind of performance takes additional electronic doohickeys soldered into the circuit. You'll get a lot further asking around in the Modder section, where they can point you to the right gizmos.
[...] I'm trying to find a way to maintain quality vaping at 3.7v without the battery voltage falling drastically over usage. Hopefully this makes sense.
Yep, makes perfect sense, and you are FAR from the first person to seek such an outcome. That's one of the main reasons people started building their own mods.

Again, get thee to the modder's forum, and read, read, read.