Some people use mercury bulbs and have success with them but there have been very serious problems in the past and I refuse to them, even if they have been fixed. A regular heat lamp and uvb strip has worked fine for many years and will continue to. For a 10 gallon, you should be fine with a 75 watt basking spot lamp. The distance the uvb bulb needs to be depends on the strength. A 10.0 uvb bulb should be 12-18'' from the dragon although a little closer is fine. There is such a thing as too much uvb in a small, enclosed tank especially if you have a translucent or silkback.
I've noticed a trend towards hotter hot spots recently and am not sure why this happening. 110 in 10 gallon is a bit high. I would dial it back to 105 and no more than 100 for large juvies and adults. They are arguably few better dragon breeders than the Dachius (responsible for the introduction of leatherbacks to the US) and they actually use even lower temps believing it is much better for the dragons as well as the gradual warming up that you use
Keep your ambient temps during the day 74-78, certainly nothing over 80. I would turn the heat lamp completely off at night, they are fine with night drops as low as 68, although 70 would be better. It's a little harder to regulate cool temps in a 10 gallon.