You can do the Underdome too - faster loading than T-bone 
Before the chest at the Vault, I found that the Pack wereskags in the zombie DLC dropped artifacts like candy. Four of them, so a fair chance to pick up the one you’re looking for per run. But yeah, now that Vault chest is the easiest way 100%.
I recently went through them twice.
0 Artifacts dropped.
Random loot is random. I just happened to get a bunch of random zeroes in a row…
Just tried the T-Bone junction, exit, launch, Vault and it worked as advertised, 7 chests ready to loot.
Not the same as the Gift Shop, but guaranteed artifacts. Not necessarily for your character, but on-level with you.
–RoA
In a few runs I did, it seems to always have:
- one chest containing a Gearbox legendary and an eridian weapon (does this happen for all characters or just Lilith??)
- one chest containing 4 COMs/shields
- one chest containing 2 elemental artifacts
- two chests containing 4 pistols each
- two chests containing 2 non-pistol guns each (SMG, shotgun, sniper)
So - it’s a great place for a bunch of pistols. Not so much for anything else.
Since I see this every time with Mord, I’d say every character.
The rest of your list is identical to what I’ve seen.
Just did this with my Siren who completed Pt.1 in the remaster:
- Fast travel from to vault from Underdome
- Seven chests
- Two artefacts (for Hunter)
- One levelled (!) Baha’s Bigger Blaster (level 44 - was not expecting that!)
Then with my siren who was imported after completing Pt.2 on original:
- Fast travel to Vault from Fyrestone
- No chests
- Fast travel to Underdome
- Quit and restart
- Fast travel from to Vault from Underdome
- Chests!
- Two artefacts (both siren)
- Hive Rhino (levelled)
- Swift Equalizer (level 66)
- Fast travel to Tartarus Station
- Quit and restart
- Fast travel from to Vault from Tartarus Station
- Chests!
- Two artefacts (one siren, one hunter)
- Hive Rhino (levelled)
So, looks like travelling from any DLC location works.
Edit: Just checked, and Jakob’s Cove also works. Plus, if you’re not a DLC location when you start the game, you simply need to travel to one and then FT to the vault - lo and behold, chests!