Yes, Scenarios have a pool of investigators to choose from, and there are special rules on what can be carried over (there were Leagues where you were allowed to carry over *everything* - French 2nd League for instance; needless to say, once you were a little skilled with the game, everything was so totally boring that it wasn't worth really playing them).
As for the doom track not filling up: first of all, the doom track very often fills up if you don't know what you're doing, and start closing gates without having enough clues to seal. This is the typical noob error, but it's not your case. Then, the doom track can become a problem mostly because some nefarious Mythos cards adding two doomers to the doom track (mostly rumors, but add MH in the mix and you'll see some HEADLINES adding two doomers), rifts moving (Kingsport Horror), more unstable locations (add Dunwich) and so on. Point is that games only with core Arkham and Innsmouth are somehow lighter on the doom track: in Innsmouth and Arkham you have a total of six high freq unstable locations (Independence Square, Witch House, Unvisited Isle, Woods, Esoteric order of Dagon, Devil Reef), so that the other unstable locations are somehow less threatening, and if you're playing wisely you can really control everything, so that the DOR is actually more a problem than the doom track. Plus, it depends also on the AO you're playing with: if you go with Cthulhu, you'll have much an easier life than if you go with Rhan or Yig. Plus, there are some AOs in Dunwich and Kingsport you'll have a nightmarish time against.
Out of curiosity: when you play Dagon, do you remember to add a doom token every time the terror level rises and at least one investigator can't discard any clue? I found Dagon games to be a little more challenging for the doom track (nothing that you can't handle properly, but still)
Finally, if you're going to play with your friend and he's good, don't go with the dream time. Go with something like Roland, Hank, Minh, Norman. They are great, but if leave Patrice at home, everyone'll have a better time, I think