Reaper will do it. You have to set it up as an "Input FX". When you arm a track in Reaper, a second "fx" button appears. This is the input effects. Using Guitar Rig in this manner actually records the wet signal.
If you use the standard way in Reaper, it will record the dry signal, but it will seem like it's recording wet as long as the regular effects plug-in button is enabled and Guitar Rig was selected. You can Render the track, which creates a wet track or you can render the output kind of like Boucne fashion in Pro Tools.
It's easiest to think about it this way. Guitar Rig by itself uses the ASIO connected input, which is whatever you plugged into the USB. when you have recording software open, guitar Rig has to use that program's ASIO connection. I use Reaper, as I stated above. What this means is that Reaper is sending Guitar Rig the signal. Not ASIO. Guitar Rig returns the signal back to Reaper. Reaper returns it to the soundsystem via ASIO somewhere in that chain. Guitar Rig is isolated from ASIO from what I understand.
The reason that your RP255 worked is that it was the interface pre-USB. The recording software is taking that signal (using ASIO to do so). Guitar Rig never is and never was an interface. Just a bit of software using ASIO exactly how Reaper uses it. Just for different purposes.
For Audacity, see if there's an input fx chain? Reaper is dirt cheap, btw. $40 - $60?
"I wonder if a composer ever intentionally composed a piece that was physically impossible to play and stuck it away to be found years later after his death, knowing it would forever drive perfectionist musicians crazy." - George Carlin