I sympathise with the OP in relation to the time aspect of completing a faction during the Tuesday event. I have never got past about 240 in it.
However as @Dust_Angel mentions, doing them without potions is definitely not impossible. The main issue is your supply of treasures. I’ve been down to 0 shards and 0 Epic or beyond treasures, but have done them all potionless. I’m now in relative luxury with shards for those remaining.
The devs are never going to change the Tuesday faction, until at least until all underworld kingdoms are complete. They want you to spend resources/gems or pay for a bucketload of gems to keep topside. They have tried to make most of the last few delves even more RNG based, not helped players in any way (other than the Wyrmrun bugs) and have not answered this question with anything remotely positive each time it has been asked.
One thing I could see is once the next batch of kingdoms arrive, they could have similar conditions - weekend event/Tuesday rotation and underworld delves get pushed to a weekend once every few weeks. However that’s just a guess, and it’s best not to second guess much in GoW tbrh. We have no idea if there will be a delve like system for the next batch. Whatever there will be, it will be setup so players spend resources and our time will be a non factor.
If I was in OP’s shoes, I’d be doing daily delves every day possible, getting them normally to 500. I’d be looking at my gold cashflow, shards and where my kingdom bottlenecks are, then working through some of the easier PF runs to start with, which can be seen from the list posted. I’d also be going into this thread and reading how people have done the potionless efforts https://community.gemsofwar.com/t/delves-strategies-tactics-and-tips/
Do the easier ones, like Deep Hive, then build your stocks up. Do Tuesday event with a Tier 2 to L120 or Tier 3 to 160 and get shards and try and do the remaining delves over the weekend. I have had issues with that due to time, but now just spend extra gems and get them done.
Also, try and consider doing harder delves around week 7-10 of the campaign for the extra stats. 4 magic is around 40 hoard.