I've been using an alternate rule for stress to attribute for 8 sessions now.
I'm using an alternate rule based on the "2d20's momentum" system.
I never really liked the idea of character Breaking themselves by pushing rolls to begin with.
So instead, when characters Push their rolls and get Banes, I accumulate "Doom" points.
With this Meta Currency, I can damage their stats (as per RAW when character pushes their rolls) and also other things like damaging their gear, bringing enemy reinforments, adding new threats, changing the environement, adding dice to opposing NPC's rolls, etc.
On the other side, when character get extra successes they gain Momentum meta-currency which they can use to add to future rolls.
So far we're all enjoying this very much and it integrates without a hitch to the system.
P.S. I encourage you using a glass bowl in the middle of the table and some form of bennies (coins or beads or whatnot).
I can vouch the fact that the peculiar sound the benny dropping in the glass bowl makes creates a pavlovian joice in the players' psyche
Note: Year-Zero Mini uses a similar mechanic.