I thought the house bassist uses Silver Slaps.
A double bass is such a classic instrument that it can open a lot of doors. I'm not very good bassist and I never make any attempt to network; still, I get offered more gigs than I can take on, so I end up declining some quite nice ones (and well-paid too, & some abroad stuff). This is because the bandleaders want a double bass rather than EUB or bass guitar. The style is jazz, swing, rock'n'roll, "postmodern jukebox". (Not intending to discourage anyone from taking up EUB - just giving a perspective.)
Something like this:
https://www.thomann.de/gb/thomann_rack_case_2u.htm
https://www.thomann.de/gb/millenium_rackbag_2he.htm
How big is it (how many "units")?
Particularly if singers are involved, you'll do well to be familiar with the American Songbook. A crash course would be to listen to Ella's records all with the similar name: "Ella Fitzgerald Sings the [Gershwin/Cole Porter/etc...] Song Book".
I sometimes use a simple overdrive pedal, but otherwise I'm plugging straight in with my P bass with flats. Sounds so nice I don't feel the need to adjust anything at all.
Does a combo exist which has an input impedance of more than 1MOhm? If not, either you will be happy going straight in, or you will have to bring your Tonebone.
I think RCF 732A (17.8kg, £742), HD-32A (18kg, £818), or QSC K12.2 (17.7kg, £709) is a fairer comparison - so heavier but cheaper. The FR800's weight at 15kg is hard to beat!
Love my BB735A and BB434, so another vote here for Yamaha.
Another option, if you are patient/lucky enough for one to come up, is a used Maruszczyk Jake.
You have a rack preamp so are you also looking for a rack power amp? If so, and if it was me, a Crown XLS 1502 would be on the shortlist. There are also less- and more-powerful variants within the range but the 1502 is a good starting point.
Another possibility (depending on the amps' input/output features) is to connect the line out of amp #1 to the line in or effects return of amp #2. What are the amps, and why do you want to do this? Knowing these details might help to find the best suggestion in your particular situation.
I have gigged with both RCF and QSC, and either will be a good choice. I used to play a similar-ish rig to you (Shuttle 9.2 + Big Baby 2) and now I use a RCF 732A.
The RCF has a simpler panel - fewer inputs, no digital menu, no "scenes" (eq profiles), no summed output. For me that is a plus; for others, they will prefer the QSC.
The handles on the RCF are a better size, in a better location, and there are more of them.
I'll offer two options:
1. Boss LS-2 which allows you to match levels between two (or three) basses.
2. A passive AB switch (e.g. this one) into a Zoom MS-60B which digitally stores multiple presets for levels, eq, or any other effects. To switch basses, you'd stomp once on each pedal.