I have the VR4geniii's and tried to biamp in a similar way. I used a SS amp on the bass units, and a TAD 60 on the mid/tweets. The TAD 60 has a volume pot and when wide open it's more sensitive (ie louder) than my SS amp (Eagle 4). It seemed like it would work out ideal. What I found was it was too hard to get the volume balanced out to a level I was satisfied with, and bottom line that biamp combo didn't appeal to me as much as my normal vertical biamp setup using 2 Eagle 4's, nor was it as appealing as the TAD 60 driving the VR4s full range. Indeed, using my TAD 60 in triode mode (30 w/c) really made the VR's sing, but at the end of the day I went back to the vertical biam setup using 2 identical ss amps (see my system).
So, the point is you'll need to be more patient than I was in getting the right balance setting on your Tube/ss biamp arrangement. But, if you haven't tried it yet - give your VR's a try using your tube amp full range.