I mean, there’s a lot to unpack here, but I’ll prefix this with the universal reminder to keep conversation cool, calm and collected. Discussing Discourse features should not be a fraught experience. 
The category moderation seems to be a small part of what your OP raised and it’s a shame to distract from that, but just in case you missed it:
You can manually grant TL3 from the admin/user/ page for a user, as well as lock a TL to a lower one if, for instance, someone attains one but turns out they can’t be trusted with the added perks it brings. Have you considered manually bumping your category moderators up to TL3 so they can move topics between categories?
Admittedly Slow Mode is currently a TL4 feature and you may not want to grant those abilities sitewide, but (as I mentioned previously) I think there is a good case to be made for allowing that to be a cat mod perk if you create a Contribute > Feature request for it.
Are there any other abilities you think are missing?