If you're doing it to study the protocol, that's fine by me, although it seemed more of a practical need to be able to control the air conditioner from more than one remote control, rather than a study or academic curiosity (after all, understanding that specific protocol won't do much good for any other project, except to understand how sick the minds of air conditioner designers are 
).
I can tell you I've often dealt with remote controls, even different ones (for example, I made a remote control repeater for Sky decoders, first SkyHD and now SkyQ), but the air conditioner ones are "tricky" based on what you've seen yourself: they send complex packets with all the settings, and at the end I have bought a "compatible" remote and I'm done.
As for "universal" air conditioner remote controls, it's very likely that among the 5,000+ models claiming to be compatible, the coding used for that specific air conditioner is included. I've often seen multiple models and even multiple brands adopt the same protocol (probably to use more or less "standard" chips). So, while I can't guarantee that a certain "universal" model will work for your air conditioner, I'd say there's a good 80% chance it might. After that, you generally have at least 15 days to test it and, if it doesn't work, return it to Amazon and get another one.