Really interesting! I also have a fireplace that is on my list of things to control. I've ordered a Broadlink RM2 Pro and am hoping that can do the job (both for the fireplace as well as a projector screen), but if that doesn't work then I'll probably build something like you have. Would be interested to hear how you 'sniffed' the code - I tried it once without much success, although I may have had a faulty module.
I use a number of ESP8266 and arduino pro minis via mysensors, and have that all integrated into Vera. Although all my kit operate as sensors (eg temperature, door, etc) you can create 'actuator' modules that can be used to switch lights or send IR or no doubt RF commands (eg
https://forum.mysensors.org/topic/682/relay-actuator-sketch-auto-off-function/13). If I had your issue, given I'd be using mysensors, I'd probably just hard code the multiple code sends into the mysensor code itself....
Anyhow, my fireplace remote has discreet buttons for on/off etc so I don't have your issue, but you could probably consider using a scene that, when activated, just sends the command to the ESP8266 multiple times. That scene can then be assigned to a button if you use something like ImperiHome. Actually, ImperiHome can also assign http requests to a button so you could use that instead.... Only issue there is of course you can't create a scene in Vera that turns on/off the fireplace.
