My friends and I have recently decided to take up playing D&D after a 4-5 year hiatus and have started by making level 4 characters and jumping into Thunderspire Labyrinth (H2) (Only campaign I had left from so long ago)

By the end of the module, they were only a few hundred away from level 10 (party of 3, bumping it up to my making a 4th for one encounter where it was absolutely needed) and that's not including any random encounters or sidequests other than Paldemar for the Mages of Saruun (Which I felt were pretty necessary).

Considering this is a campaign meant to take them from 4 to 6 (maybe 7), something seems seriously off about the amount of exp per encounter. We had planned to play through Pyramid of Shadows next, but at this point we're better off just starting on P1 rather than H3. I know the common solution is to just not use experience as a lot of people choose to do, but I really don't like that idea. My friends and I are hardcore video game RPG fans (mmo and otherwise) so experience points are pretty much a necessity in all the party's eyes.

The module gives me the amount of collective experience the encounter gives based on the experience per monster. So as an example, Encounter H8: Murkelmore's Chamber has 2 level 6 brutes, 1 level 5 controller, and 1 level 7 Elite soldier. The encounter has a total of 1300 experience collectively. I deal out the experience by splitting it 3 ways for 3 party members

I should say that even being level 9 on the final encounter, the party still almost died, but I don't want to start H3 now and end up being mid-late paragon by the time we finish. So I'd really appreciate it if you guys could help me discern a solution to this problem.