I took your ideas to heart and modified my house rule. The current version has only one action to get rid of banes: breaking banes.
Break Bane
Each bane has CR = 12 + attribute score with which it was inflicted.
Describe your actions as to how you want to break the bane and choose an appropriate attribute. Make an action roll with that attribute.If the result is greater than or equal to the CR + 3 times the burden of the bane, it is broken.
Otherwise, if it is greater than or equal to the CR, reduce the bane’s burden by one.
If it is less than the bane’s challenge rating, increase the bane’s burden by one to a maximum of three.
You can choose to break multiple banes with one action. If you do, choose a separate attribute for each bane, and roll for each bane individually. However, because your attention is spread thin, you gain disadvantage equal to the number of banes you are targeting on each of the rolls.If you break a bane this way, you figure out how to counteract it, and any time the same character inflicts the same bane on you, you get advantage 1 on rolls aimed at breaking it.
So, I changed the name from sticky counter to “burden” and tried to address some of the comments. It is now basically a version of this suggestion, with the addition of burden, multi-targeting malus and a kind of resistance once you finally break a bane.
Contrary to the linked post, I chose the formula 12+attribute, because I think, that getting rid of a bane inflicted by peers should not change the probability of success.
Take a look at the probabilities to beat CR 10+AL (P10) and 12+AL(P12) with an attribute of AL:
AL P10 P12
0 55% 45%
1 66% 56%
2 65% 56%
3 65% 55%
4 64% 55%
5 70% 61%
6 73% 64%
7 75% 67%
8 82% 75%
9 86% 80%
So, for AL 1-4, the 12+AL formula gives you about 55% percent success probability if you can match that attribute level.