While a UTH will provide an adequate warm spot for belly heat, it's not going to do much to raise the ambient temp. The ambient air temp throughout the tank should be somewhere between 75-80F. If you keep your house on the cooler side, and the ambient temps won't stay above 75F, you still may need to use the lamp for supplemental heat. Some things that may help are covering most of the screen with aluminum foil, plexiglass, or you can even cut some linoleum floor tiles to fit. Just make sure they aren't sticky on the bottom. This will help with humidity, but with such a large tank, and especially if you still need the lamp, you may need to mist the tank once or twice a day.
Also, once you start using a UTH, make sure your substrate layer is only about 1/2 to 1 inch thick. Also, if you are having a hard time finding a UTH to fit, you can try the Ultratherms from Reptile Basics. They come in longer sizes. If your tank is anywhere between 36-54 inches long, a 11" X 17" UTH will work fine, and most brands have this size.