Bloodweb grind idea
One probably easy fix to get control of the grind:
When a character has a teachable unlocked, the icon on the overview changes from the lock symbol to a checked box symbol. Make it a real checbox you can uncheck, so it stops from appearing on others' bloodwebs. As soon as you check it again, the perk can appear again.
Wouldn't force anyone to have a perk slot blocked in the web for not wanting to unlock a teachable while leveling a character, and would allow you to have only the 14 + X perks appear while you are leveling a character. This way a lv50 character has a way higher chance to get at least some of the perks you want, and after that you can activate the perks again to level up the character further.