Views are obviously something different and it sounds like you figured that out.
Reflection in the floor using the Shaded with Reflections setting depends on a model display setting in Options.
This is -not- the rending floor, but the "orientation" you want to use for the shadows and reflection in the realtime rendering mode.
As for the room for actual rendering, you can orient the room independently from the model:
Go to the Render>room tab to open the dialog. Now -uncheck- the Lock Room to Model checkbox; make sure you are in Model orientation; use the rotate sliders to know know which slider you need to move 90 degrees; Recheck (!!!) the lock Room to Model checkbox (!!!) and now you can move the model and the room moves with it. Now when you render, your floor is where you re-oriented it to.
Play with this dialog. It is intended to do some specific re-orientation or you can do creative orientations. This is a very old function and little has changed in last decade or two except the interface is somewhat improved (I'm being generous here). In all, you have some pretty good control over the environment but no matter what you do, Photorender is an outdated tool that only does so-so quality images as output. Photolux (extra$) does better but I cannot justify the expense. In general, you can do this but often, life is simply too short to get something high quality out of it.
