How would I begin to reverse engineer the protocol when I get the controller?
One way or another you're going to need some gear, probably a logic analyser (LA) and/or an oscilloscope (CRO). Not as scary as it sounds because these days you can get them really cheap as a USB device for your computer.
If you're into embedded electronics this will be a usefull tool in future anyway.
You need to know two things, the voltage level on the comms lines, and of course the protocol.
I'd start by opening the controller box. Look for a chip mounted next to the connector where the wire is plugged in. If you're dead lucky it will be a MAX232 or MAX485 or some easily recognizable chip. If so then you know the voltage level of the physical connection.
If not then that's where the CRO comes in, just put a probe on the line and read the voltage. The only reason I say to get the voltage is that I'm used to using an LA that can only handle 5v on the inputs. Truth is if you get a CRO with storage facility (which these days they probably all have) you don't need the LA because that's really the same thing.
Use the CRO to identify the data line(s), having done so connect probes to them and start pressing buttons. Note the patterns that go out and what is returned.
There'll be a frame of some kind going out and an acknowledge coming back, very quickly I suspect you'll start seeing a pattern.
Once you've got it documented you can duplicate it with the Arduino.
Caveat: It's possible that it's some weird-arsed Manchester-encoded encrypted synchrounous protocol based on HDLC with an X.25 twist. In which case it may be too difficult to figure out, but I think that's unlikely.