I thought I'd update this (not seeing any replies). TL;DR -- I had to replace both the regulator and motor, and was able to DIY it.
I first bought and installed a new Mahle-Behr aftermarket regulator. This caused the blower to run, but randomly, including sometimes with the engine off. I removed the blower fuse -- location shown in the owners' manual -- to save the battery and took the car to the dealer. The dealer, using its PIWIS, diagnosed a short in the blower motor. They recommended a new blower motor and regulator, saying that the failing blower motor short could have damaged the new regulator and that it would be most efficient to change both at the same time (I agree with this last part, at least).
The dealer wanted nearly $2,700 to provide and install a new blower motor and regulator, including almost $1,800 for the parts. I balked at the parts price and decided to attempt the work myself. I was able to easily find the Porsche genuine regulator and blower motor for a total of $900 (getporschesilverspringparts.com) and to install both of them, and to clear the codes with my Autel device. Everything works great now, fingers crossed. Many thanks to those who provided detailed guides here.
What I didn't see here was how to replace the blower motor. The steps to get to the motor are the same as for the regulator, but getting the motor out and in is a pain because it is very tight fit, particularly the installation. The Pelican Parts guides for a 991 are helpful, but even they don't show how to get the motor out and in from the housing.
I'd add the following tips for the whole operation based on my limited experience (this is for a LHD US car), to the extent they are helpful to anyone attempting this.
- You don't need to remove any of the dash vents (I saw somewhere that somebody recommended removing one of them).
- To remove the cupholder mechanism, you need to push up on the two spring clips as shown in the DIY guide here. That required a surprising amount of force to push them up.
- Once all of the screws holding the glove box to the dash are removed, you may need to pry the top of the box down from the dash because there is a clip/guide near each top corner of the box holding it to the dash. Use a trim tool.
- You don't have to remove/detach the electronics from the inside of the glove box (which I couldn't pry out), or even the footwell light, to replace the regulator or motor. Rather, I rested the glove box on a cardboard box after detaching it from the dash, which left enough slack in the wires to avoid any damage and just enough room to complete the other tasks. Mind the wires for the glove box light as they detach easily.
- Lowering the passenger knee airbag was a bit scary, even though I had disconnected the negative battery cable, but I think it is impossible to get the blower regulator and motor out without doing so because the airbag blocks the air duct you have to remove. You have a lot more room to remove the duct, regulator and motor if you remove completely the two screws holding the bag and lower it to the floor -- again, no need to disconnect any wires. The airbag is held with two E30 torx screws, which the manual says should be reinstalled with 13NM of torque. (This is the same prescribed torque for the two E30 screws holding the glove box, but the T25 screws take only 3.2NM.)
- Once you get the dash and airbag lowered, and the floor vent tube wiggled off, you can remove the regulator and blower motor.
- You need a long T20 or extension to reach the four screws holding the motor, some nimble fingers to make sure you don't drop them into the dash, and a ton of patience to wiggle the motor out and in of its housing and the dash. It pulls out a bit and down, and I had to navigate a set of wires to the dash airbag mechanism which interfere with the removal and installation.
- JR Richardson's videos are also a godsend, and point out that the relevant parts and configuration of the 981 are the same for a 991, so guides for the 991 that you find on Pelican or elsewhere are equally helpful.
- The whole operation requires a lot of back-bending and reaching, which probably would be easier if the car is on a lift (I don't have one). It took me about 3.5 hours the second time to change both the regulator and blower motor and put everything back, but it would've gone alot faster with an electric driver/screwdriver. There's just not a lot of room for a ratchet for the screws holding the airbag or several of the screws holding the dash. I think the dealer said it takes ~4 hours, so I guess I wasn't too slow.