In a multistage heat pump system the thermostat (Braeburn 1200 or 1200NC) has wiring terminals as follows:
R O B C Y1 E/W1 G W2
Currently there's a jumper between E/W1 and W2 (Exhaust and 2nd stage heat control)

The thermostat I'm installing (Lux TX 9100E) has these terminals:
A RH W2 RC G Y W1 O B C

Any thoughts on how to handle the jumper in the new unit?

One diagram I have shows the Heat Pump unit 24V going into Y with a jumper to W1 but this configuration has an auxiliary heat 24V going to W2, which I don't have.

Another shows the Heater going to W1 and the AC to Y but this one has a separate transformer for Cool and Heat (going to RH and RC respectively).
If I assume the Y line from my initial configuration is the AC transformer, this last setup makes sense. I just need to run a jumper from W1 to W2 to account for the 2 stages of heat.

How did the old one wire up? To me it looks like you should be able to match wire to post on each. You can add a jumper wire from W1 to W2. You will need a jumper from RH to RC.

Yessir, that's what we did.
Now it seems like something's interrupting power to the outdoor unit. Prob'ly should've tested the transformer in the heat pump unit FIRST.