Now I'm curious. (Because I was planning on jumping ship to Linux!)
Are you saying that you select your AVR in Reaper Preferences/Audio/Device page from the device drop down menu. Then you go to assign output channels on the master (or a different track) and it only shows two channels of output on that AVR? In other words, the AVR identifies as a two channel device in Linux?
There isn't any way for Reaper itself to influence the driver connection with an audio interface. You connect the interface to the system. Reaper or any other audio app has access to the resource via your OS. I don't mean to suggest a bug in Reaper is impossible! Just talking through the expected scenario in case it leads to a revelation.
If you were maybe selecting <default system devices> in Reaper preferences instead of your AVR directly, that would use your LinuxOS audio control panel instead. This might be more limited? Did you try selecting the AVR itself in Reaper? Is it an option? (ie. Is your AVR in the device drop down menu?)