The thing is – with Brunner’s base only the default button layout of the TM Warthog (or any other joystick selected from the list) is supported. Any additional buttons are simply not mapped and not exposed to the sim (or to the Brunner’s CLS2SIM app).
I solved the problem with Autopilot settings – I set “Percent of way used by AP” to 10 in Cessna 172 by A2A (instead of 100). Currently, simulator trim while on AP matches CLS trimming.
Had the same problem with A2A’s Cessna. Try setting a different value to “Percent of way used by AP” in the Autopilot tab. Cessna works well with something between 90-93. Those values apply for a linear response – you may need different values if you use non-linear response curve.