I sort of play bass as I always wanted to try something different. I started with a cross over bass (Ibenez 6 string , short scale ) it plays well and sound great similar to a baritone guitar. I started with using a Mark V and or Roadster and it just did not sound as effective as I wanted. OS Recto 412 cab loaded with EV speakers. Bought a low cost fender bass amp with a distortion built in, not very satisfying. Wound up with a Mark Bass JB player and added a 410 cab and that simple rig sounds great. Now I have a 4 string long scale bass and a 5 string long scale. I do get your point that the natural harmonic content you get with tubes is unequaled. So the guitar amp was a novel idea. If that works for you great... You could run it parallel to the 400+ amp (you would need a isolated signal splitter to eliminate ground loops (one circuit is direct and the other uses an isolation transformer, reference Lehle P-split II, I use one of these to run two amps in parallel or I have used it to slave one amp using the FX loop of the other).
I did consider a Mesa Prodigy or Strategy bass amp but I am uncertain how much I am into playing bass. I do on occasion just that but most of the time I am playing guitar. Then I had the bright idea to play drums. Now that is totally different. I now have a different perspective on things, guitar, bass, and drums than I did before. back to getting that tube tone into a solid state bass amp I have been eyeing up the LeBass tube pedal. This has some cool features to it that may be used to capture that harmonic distortion (non-linear) that you can only get with a vacuum tube vs what you get with solid state. I may think it over and try the pedal first....
https://www.sweetwater.com/store/detail/LeBass
So that pedal may help my rig out. May even work with the Bass 400+. While I was considering some alternate form of amp for bass, I was looking at the Mesa web site on the tube bass amps and in one of the videos they used the flux drive with the strategy88 You can see the bass player trigger it on in the beginning of the clip. I have the flux drive and grid slammer and they work great with the Mark series amps. I have not tried it with the solid state bass amp. I also have a plexi lead pedal (Wampler) that I bought to try to get a Marshal tone out of my RA100 head, needless to say the amp sounded better than the pedal. So what I did next, ran it in front of my bass rig and that was great. Still not perfect so a tube preamp pedal may work out better. All you may need is the flux drive or grid slammer, perhaps the throttle box may do the trick and they will not take up much space either. Here is a link to the Mesa Strategy88 video using the flux drive. That may be all you need. Just an idea.
http://www.mesaboogie.com/amplifiers/bass/prodigy--strategy-tube-bass-amp-series/bass-strategy-eight-88/index.html#videos
If your amp does not get the dirt, the flux drive will provide the Mark series tone but without sacrificing the signal loss on the low frequencies since the preamp section of a guitar amp was not tailored for bass guitar. Wonder how the preamp of the Mark would sound if channeled into the Bass amp. I did see the 400+ is using the 6L6 tube so it may be okay to use the guitar amp.