So I obtained a replacement capacitor. The old one (Yuhchang, top) and the new one (Cornell, bottom) are pictured. A quick snip with the soldering iron, and it has proven to fix the motor: no more buzzing after a few minutes of operation. Good!
Now, back to the automation part. I'm still mulling over whether to make a new circuit board (6 triacs for the motor speed, a relay, a triac for the dimmer, an esp8266 w/ some gpio), or just leave it as-is cuz its working. So to experiment, I have acquired 4 zigbee light-bulbs . I went with the Home Depot EcosSmart connected lights (each is zigbee controlled on/off/dimmer). This would give me automation on the light part of it.
Now, i have to convince my Xiaomi Mi Home Gateway to pair. It was trivial to pair to all its own widgets (there is an app, which can be set to 'mostly english' mode).
But what is this? Sacre bleu? There is no 'light'. (Although I am glad there is a zero-fire option, that's what i'm looking for in electronics!). Hmm. I've tried a few different ones. The light bulbs are a bit of a PITA to get into pairing mode (you turn them off for 5 seconds, on for 5 seconds, repeat 5 times, then wait, then it blinks). Hmm. More research will be required.
Now, i do have this gadget, which i've not tried yet. Its a USB zigbee sniffer. it shows up on USB as Product: CC2531 USB Dongle, Manufacturer: Texas Instruments, 0451:16ae, and its one of these. And I think this is the user guide. Hmm. I'd rather not have two 'hubs', I would prefer the Xiaomi gateway handle all the devices. Hmm. It seems the Xiaomi supports ZHA profile, which means it can support the lights, just have to figure out how to force it to pair. Suggestions?