I've got it locked in stomp A, then it stays detuned even when you change rigs. It's worth giving up an effect slot for.
This is how I have mine set up as well (Stage). Additionally, I have Stomp A assigned to the Looper button so I can easily change from standard tuning to Eb whenever needed. I don't use the Looper so that button assignment works best for me.
Because it is locked, it will stay in whichever tuning you have selected, no matter which rig or performance you change to.
(i.e. if it's in Eb, it will stay in Eb throughout any rig and/or performance changes until you switch it back on/off).
I was looking for the same solution that the OP is asking for, and this is the best workaround I've been able to come up with.
Yes, it still occupies a Stomp slot, but with assigning it to the Looper button, I still have the I-IV switches fully available.