When I first started using Reaper I noticed that things would distort and sound bad especially after adding some plugins. Compared to the rest of the computer's audio output Reaper is way hotter. Regardless of listening environment and sample rates RENDER did at one time not ever equal what I heard when I hit play (crud in the mix & oversaturated upon render.)
NOW, I don't have this problem anymore, though I can't claim I really fixed anything. Two things have changed:
The most important being that I started mixing "in the green," meaning never let your tracks hit yellow or red on the meters... MASTER included at first until you can bring up the overall volume with strict control in the end. I like loudness or limiter plugs on the end of the master channel to bring the volume up to par, find one you love. This eliminates a lot of potential "digital-y" drive in the mix and apparently the rendering process (not that I know why, but certainly experienced this first hand).
Secondly I now have 16gig of fast RAM w a collection of plugins I can trust to work. Plugs can sometimes be the culprit.. especially if they are older than Reaper 4.x.
In a way I am still not sure that my render is precisely equal to playback, but I love my rendered files enough to pump 'em to peeps... benchmark met! I see the OP found an OpSys thing.. so I guess this was different. You can always drop your bounce into a track and bypass the parent send and send to your hardware so you can A/B... in fact there is a checkbox to have Reaper do it for you (you still make the sends).
Happy Mixing