That would be at least 270 degrees. It seems most are 90 degree throws, you'll have to specifically look for one with enough range - you probably don't want continuous, because on those the signal is proportional to their rotational speed not their position.

I would get an FrSky Xlite, but that's because I'd use it for other things too. It would unfortunately eat up a substantial amount of the budget :( but it is an awesome little TX.

You'll need at least 6 channels, but the more the better. The Turnigy 9x has a decent reputation.

https://hobbyking.com/en_us/turnigy-...-firmware.html