Biamp question

Honestly I am not sure how to use the built in crossovers of the speakers. Seems the connections would be different. Please excuse my ignorance on this topic. 

I’ve never used internal XOs (I built my speakers without XOs), but my understanding is that they are in the speaker, so if you connect to the speaker terminals you will be using them.

So you could just connect the Parasound to the LF terminals on the speakers and the Rouge to the HF terminals, adjust the Parasound to match volume, and you’re done.

But I've never done this so if I were you I'd wait for someone else to confirm

Now I’m thinking/wondering if you need to have 2 amps that are exactly the same to use internal crossover wiring method. 

I have a pair of custom speakers that are very similar in design to the Legacy Focus using Eton drivers on top and Peerless 1259 12" woofers.  The Peerless are a bit less efficient so bi-amping is pretty much a necessity.  I've used the internal crossovers without issue.  Since the bass drivers are less efficient, I've always used separate volume controls for the satellite section (tweeters, mids, midbass drivers) and the woofers.  

My sources have all had built-in volume control so that has been the main volume control while the bass section has either been an integrated amp with its own volume control or a separate preamp to drive the woofer amp.  Currently my DAC is an Audio Alchemy DPA 1.  I run the balanced outputs to a Red Dragon S-500 driving the satellite section while the RCA outputs drive a Kingrex PREference preamp into a D-Sonic M3a-800S.  This allows me to adjust the bass output to suit my taste.  The Kingex is fairly cheap but is quite transparent and articulate in the bass range so works very well in this application.  You could try biamping first with your 2 different amps using the 2 pairs of outputs from the Rouge preamp and see how that works.  If the bass isn't satisfactory, then you could do as I've done and ad another volume control device between your pre and the bass amp or perhaps you could do that from your source to avoid running the signal through 2 preamps.

You’re fine OP. You don’t need anything BUT two amps and cables. You have a good idea. SS for the bass and Valves for mids and highs. The Parasound will have the greater gain. It is a plug and play thing. It will take more time to route the cables than anything else. Remove the jumpers between lows and highs on the speakers and plug in. Adjust the Parasound. DONE.

Side Note:

You need two of the same for vertical bi-amp. You're using them horizontal. I've biamped for 40 years horizontal, NEVER vertical.
I quit using Valves for bass 40 years ago too. Just a bad idea in reproduction, not to mention the heat.
Only one time I didn't bi-amp and I fixed that soon enough. BIG fan of bi-amping with SS and tubes. 

I forgot, Merry Christmas and Enjoy...

Regards