you don't mention your budget, or which Von Schweikerts you're using. I experimented with biamping my VR4genIIIs - and have a TAD 60 tube amp that I used on the top end with a Electron Kinetics Eagle 4 on the bottom. The TAD 60 is fantastic, especially for the money (look through the forums for rave reviews, and they can be found used for ~$800), but I was not overwhelmed with the results from biamping in this config - I concluded it was more trouble than it was worth. However, driving them with the TAD 60 alone is wonderful. I also obtained better results biamping them vertically with 2 Eagle 4 amps. My primary issue with the horizontal biamp using the TAD/Eagle was tuning them to balance. I got out my sound level meter and frequency generator to balance them. I was using the speaker's internal crossovers and the volume pot on the TAD to achieve the balance. It was nice, but was a pain. And as I said, the results not overwhelming so I abandoned the idea.
I'm not trying to discourage you, since I'm sure beter results than I achieved can be had with more patience. No doubt my room also presents some challenges. At the very least, you have the chance to put tubes on your VS's - which can be excellent.