Actually, you don’t need to cannibalize a remote if you don’t want to… I also have a Hampton Bay RF controlled ceiling fan that works on 303.875 Mhz, so I got one of those generic 315 Mhz RF transmitters/receivers from Amazon for hooking it up to an ESP device (an already existing Sonoff Mini R2) and made it fully working with ESPHome (no MQTT involved at all).
If the 315 Mhz RF Transmitter doesn’t work for you out of the box, you’ll probably have to replace its SAW resonator with the correct one for that frequency. You can get those from AliExpress or from an old/non-working remote.
You can see more details on this post.