Sizing a heat pump heater to replace a resistive heater in a custom gunite spa

I'm hoping to get some advice on how many BTUs I'll need to heat my spa.
I've never used the spa (I've been restoring it for the last 3 months), so I can't rely on past experience. I just did a few brief test runs.

What I have

• Approximately an 850 gallon in-ground gunite spa, about 8' diameter.
• I have a vinyl cover (4-5" thick) that sits on top of the brickwork (probably a fairly good seal).
• Insulation is mediocre (I installed some R-6 panels around the tub when I had to dig up the plumbing), about 2/3 of the way down the sides, and insulated the buried pipes (spray foam).
• Existing heater is 11kWh resistive (CSPA XI). Both elements burned out yesterday and I might as well get a heat pump.
• When the heater did work, it was warming up a full spa at about 1.5 degrees/hour (from 70F).

So I'm thinking as follows:

1. The people that built this thing thought that 11kW was enough.
2. Resistive is 11Kw (or 38000 BTU) in any season. Heat pump won't work as well when it's cold.
3. My location is Asheville, NC.
   1. Winters are typically mild, with occasional frost, cold nights and warmer days.
   2. Last year we had 4300 heating degree days, averaging 360/month, peaking at 900/month.
4. I'd like an inverter model (so it's quiet in my back yard). I am looking Raypak Crosswind (I-40? I-50?)
5. I'd like to be able to use the spa for 80% of the year (and wouldn't mind 100%)

Should I oversize it? (and are there downsides to that with an inverter?)
Should I be aiming for the BTU output at the coldest air temps I expect?
Is there a reasonable formula for sizing a heater given the parameters I know?

Thanks!