Best way to farm Frozen Winterfest Wishlists?

Hello there! Long-time player, first time poster!
Due to a series of badly timed hiatuses or just plain holiday business, this is actually my first Winterfest. I've managed to (again due to holiday business, given how obsessively I play) get a bit over 500 Wishlists, but since I want the 3.5k giftbox, well, uh. I need to pick up pace.
My current strategy is to just find the gate with the most clockwork tunnels and proceed through it linearly, but that's fairly timeconsuming, plus I'm not the best at selecting gates, and I keep forgetting to check the map and ending up in Deconstruction Zones. One thing I've tried is finding a gate with a clockwork tunnel at Depth 1 (since as far as I can see it gives the same amount of boxes and thus tokens and is easier than my native T3) and just doing the Winterfest room if it exists and then starting back from the surface. Is this the best way to do it? Or are there others? I'd love to hear.
((I hope this is posted in the right place! If not feel free to redirect me))

Thanks!
I'm not really one for playing with people I don't know outside the game, and the one friend I regularily play with has been pretty busy & I don't have alts given that I'm a steam player, but it's times like these that make them seriously tempting!
But the gate advice is very useful, thank you! Pity it's gonna be the first to cycle out.

Running earlier tiers and easier difficulties will drop less tokens. In a single tier 3 elite treasure room, you can find upwards of 120 tokens. Tier 1 on normal? Around upwards of 20 tokens.
Thus the best way to farm tokens is to have guildmates or friends all spread out and run through tier 3 clockwork tunnels on elite. The latest arcade gate rotation gives you a slime clockwork tunnel 50% of the time and a lichenous lair the other 50% (first depth). Just run through the tunnels until you get to a room, do said room, and restart the run. When it switches over to a lichenous lair, switch up your tier/gate until you get another clockwork tunnel, but make sure to check back whenever you can for best token rewards.
If you have dedicated guildmates and good gates, you can get a box in 2-3 hours of hardcore grinding.
Good luck!

You can still have alts even as a Steam player, especially since Steam players have to make another account if they want to edit the wiki. The regular download client is used for those.

Note that multiple tokens will drop onto the same tile, so that although T1 appears to have the same amount of tokens as T3, it doesn't.
Also, it's usually faster to repeatedly re-enter the clockworks immediately after beating a danger room, rather than beating the level and going to the next floor.
As usual, get MSI Increase if you have it, avoid fighting the enemies, avoid minerals, only go for boxes if you'd like. One of Drakon's abilities can give a speed boost with the right ultimate, the other pets might have one too, not sure.

I run normal regardless of depth anyway, since as much as I love this game I'm ... really not the best at it. I dont think I'd be able to survive an Elite treasure room, since for the lack of a guild (social anxiety and a few bad experiences when I was new have left me with an inability to play with people I don't know outside of the game) I tend to solo EVERYTHING. Tier three probably should still drop more than Tier 1 though, so that's good advice.
Well, I'll think on the alt question. Not sure my computer will be able to juggle them, but I COULD try...
Thanks for the tips! I don't have any speedboost gear at the moment, but that's probably a good piece of advice to remember for the future.
Try Dark Sun gate T2, the first depth is always a clockwork tunnel and it's still relatively easy.
The easier way is to get a few friends searching and invite each other when you find a room.
But that might be harder nowadays since playing seems to have dropped off since the first week.
There's also the cheesy way which has been posted before for other events, you could bring alts and when you find a room, have them all go solo. Then finish your room, join the first alt's party, finish it again, etc.
(Or finish the room first if you can carry all the alts without lag)