I’m in a similar position, new player with Axton at 38, Maya at 14, Zero at 9. With Axton I hit 33 at the end of NVHM and went into Tina’s DLC (I’ve been playing some form of D&D for 23 years now, how could I not? 
). It’s just as hilariously entertaining as you’d expect, with one major caveat. By the time you hit the Mines of Avarice near the middle of the DLC things will get pretty annoying. I suspect the post-Forest portions of the DLC are balanced around The Bee, so if you don’t use it (I find it to be a remarkably overpowered piece of gear) enemies will be bullet sponges for you. It doesn’t help that most enemies, knights especially, are hard or impossible to crit, so if you rely on long range sniper headshots that won’t work very well. You definitely should use The Bee against named orc Warlords though. They’ll probably still level themselves up to Duke of Ork, but burning their health down as fast as possible is key. Even with The Bee a Duke is a ridiculous bullet sponge. Against other enemies, your choice seems to be using The Bee and melting everything almost instantly, or not using it and having fairly long fights. Not really the balance I’m used to in this game. For perspective, enemies in TVHM have about half the health of enemies in Tina’s DLC in NVHM.
Carlton_Slayer, at what point in NVHM do you recommend diverting to Scarlett and Torgue? Like the OP I’ve skipped them so far because they stop scaling at 30, so taking the route of finishing NVHM and then doing a DLC leaves just Hammerlock and Tina to choose from. I’d planned on doing Hammerlock on Maya when the time comes, but if there’s a sensible way of doing Scarlett earlier that sounds fun. Do you alternate between doing a Scarlett quest and a quest in the main game to try not to horribly over-level either one?
When should one do the Headhunter packs? I’ll grab those before the Steam sale ends, but am I correct in thinking that their primary role is endgame gear-farming, or are they something worth doing in NVHM/TVHM as well?
Strange- I actually like the aesthetics of Tiny Tina. It’s just something about the way the filtered sunlight happens in Aegrus that weirds me out. Oh well 
@Worblehat- I think I did them just after they became available so the late teen/early twenties levels. I switched between the main game and the dlc since I didn’t want the main story rewards to become trivial. Since I only did the two dlc in normal (and didn’t farm for anything, so I never racked up excess XP) I finished normal with everyone right around level 31-32. BTW, max levels for the Tiny Tina dlc (and I suspect Sir Hammerlock- but I never played that dlc in normal) is level 35- the Ancient Dragons can be leveled by Boost up to at least level 39 though…
)
Anyone would be selling themselves short if they didn’t experience it at least once.
The only parts I didn’t like were the walking, the fan boats (even worse than the sand skifts), and the raid boss. That and the witch doctors, but they’re child’s play with three Mayas.