Buffing Pyromancer cost will only make the problem worse.
so Pyromancer needs a tier shift upward

That is probably right, but nothing comes to mind right now.
I had only written -1 all tiers on pyro, but tier shift could be ideal.
Although, I actually don't like pyro+++ moveset much, so one higher... idk.

Maybe the new Pyro+++ should get some tele-swap squares.

You make good points in favor of tier shifting pyro, but i feel like teleswap on pyro moveset would be erratic. The only unit that comes to mind which is intentionally erratic is Bat, for theme. I'll reconsider pyro change while leaving what I have currently on the notes, and I will be posting a full balance change preview here soon. (today/tomorrow, probably)