I've actually been working at this more or less for a few months. Have not tried x84 but it looks promising.
If you want to run door games, you're going to have a bad time. I've been researching and testing the various emulation packages and haven't got anything that isn't incredibly slow due to the software emulation. I've tried dosemu with dosbox, and qemu and basically nothing will get you what you want. I talked to a guy who made more progress than me and he said the only thing he got working properly was to have a native x86 linux box with accounts setup to launch each door game that he could tunnel into from the pi hosting the BBS package. At this point, you'd probably be better off with a low-power Intel Atom box running Linux or Windows anyway.
If you want a nice BBS package without games, check out synchro. It runs, and works perfectly as far as I can tell, If you can't get telnet or other services to listen on any ports, run synchro when you're sudo'd or under root to get everything working properly.
The Rpi Mystic build will compile and build properly on the Pi and even let you go into the gui to change configs, but the daemons will not launch. Some users say you can use alternative daemons for telnet but nobody really seems to want to talk about where to get them or how to configure them. I also could not get the standard Linux source to compile or build under the Pi, the RPi package gets you the closest.
Alternatively, you could use something like qemu to emulate a whole DOS system and run any DOS-based BBS software within that virtual machine. This might get to be slow though.
I'd be interested in how the performance differences between the RPi and other low-power SOCs like the Cubieboard or Bana-Pi compare as these little boards might make better candidates.