So I found this other info that seems more credible and sort of gives some credence to what that other thread said even if it works a bit different than what it sounded like was being implied.
OK, it’s a bit complicated. 
In Normal Mode (first playthrough), completing the story missions in the main game has no effect on the levels in the DLC, so it doesn’t matter if you beat the Warrior first.
The DLC has a range of possible levels in each mode.
Normal Mode:
Headhunter packs – 15 - 35
Pirate and Torgue DLC – 15 - 30
Hammerlock and Tina DLC – 30 - 35
Digistruct Peak – 35
TVHM (second playthrough):
Headhunter packs – 30 - 50
Pirate and Torgue DLC – 30 - 50
Hammerlock and Tina DLC – 35 - 50
Digistruct Peak – 50
Within those ranges, the DLC maps generally seem to scale to your level when you first enter them, and, in Normal Mode, the map levels don’t change after that. So, for example, if you had started the Pirate DLC when you were level 15 (or below), the first map would still be level 15, but new maps after that would probably be level 30 (the limit for that DLC in Normal Mode). If you start the Tina DLC now, the first map will be scaled to level 34 (your current level), but if you reach level 35 while playing it, later maps (and the missions in them) should be scaled to level 35.
In TVHM, the DLC map levels work basically the same way, until you complete the story missions in the main game (beat the Warrior). After that, most maps and unaccepted missions in the main game and the DLC will scale to level 50. However, if you started any of the HH packs at a lower level (eg. 40), they will probably stay at that lower level.
In UVHM, everything (except already accepted missions) always scales to your current level.
FYI, the main game is going to start around level 31 in TVHM, so, at level 34, you’re already a bit over-leveled for the main game, but it will catch up eventually (you get less XP when your level is above the enemy/mission level, so you’ll level up more slowly in the main game, until the levels start to even out).
Another basic issue to keep in mind is that you probably don’t want to be too much above level 50 before you start UVHM. UVHM always scales to your level, but any gear that you find in TVHM (except in the Golden chest) will be limited to level 50, so if you level up too much from farming or playing the DLC, you could have a really hard time when you start UVHM.
Having said that, feel free to play any of the DLC in Normal Mode, but any gear you get in them will be limited to around level 30 or 35, depending on the DLC, so most of it won’t be useful for long once you start TVHM. One thing that might be worth going for is the Magic Missile grenade mod in the Tina DLC. It’s one of the 3 “magic” grenade mods in that DLC. They all slowly regenerate grenade ammo, and the MM sends out homing slag balls. It’s one of the more popular methods for applying slag. Then again, you may not be using slag much yet, so you may not have much use for the MM now, but it’s something to keep in mind. You’ll be needing slag sooner or later.
As for the 3 specific items you mentioned, the Grog Nozzle, Unkempt Harold and Rough Rider:
The GN is kind of a non-issue. As someone else mentioned, the regular GN is a mission gun, so you’ll only have it in the mode/playthrough where that mission is active (and you can’t trade it or put it in the Stash). Accepting that mission in Normal Mode only gives you a GN in that mode.
However, during the “Loot Hunt” event, Gearbox had the game drop non-mission versions of the GN that are just normal guns (can be used in any mode, etc.). You can probably get some of those from people in the In-Game Trading sub-forum. FWIW, the level is kind of unimportant (as long as it’s not above your level, of course), because the level only alters the damage, and you shouldn’t be using the GN for damage (it’s just a fraction of what you get from a regular elemental gun). The healing factor and other special effects are the same, regardless of the level.
You can get the Unkempt Harold from Torgue vendors (in the Torgue DLC), or Savage Lee, or just as a random find. The Torgue vendors will be limited by the DLC level limits, so you won’t get one above level 30 from them in Normal Mode. You can try them in TVHM, but you’ll need to get Torgue tokens first. Or just farm Savage Lee once you start TVHM (in Normal Mode, he’s going to be a very low level).
You kill a specific enemy in the Hammerlock DLC to get the Rough Rider. You can do that now in Normal Mode and get one around level 34 (your current level), or wait until you’re level 35 (the max level (more or less) for that DLC). You could wait until you start TVHM and then go there at level 35 to get one, but that will set the level for that map and it will stay that way until you complete TVHM in the main game, so you won’t be able to get a higher level one until then. So, if you want a Rough Rider now, I’d go after one in Normal Mode. Then, some time later, maybe when your level is in the 40’s, you can go after one in TVHM. Then go back and get a level 50 version at the end of TVHM.
However, I think some people prefer a lower level Rough Rider, because it adds less health (making health gating easier), so you might actually prefer a lower level version. Your call.
