The VR4 mk3 is flattish 4 ohm load. Assume it dips to 3 ohms, but we don't know the phase response of the speaker, which affects the load felt by the amplifier. I did not see a review on Stereophile.com.
Info about speaker impedance and phase as relates to amplifiers.
http://sound.westhost.com/patd.htmTo maintain a relaxed confident sound from any amplifier, you want enough headroom to allow for dynamic peaks without approaching max power, where distortion rises dramatically making the amp sound "stressed." For your dynamic but hungry speakers, sufficient headroom will be a rather high power rating, depending on how loud you play, and how your preferred music falls on the impedance curve.
With nominal 4 ohm speaker of moderate sensitivity, I'd be sticking with SS to keep good bass control at low impedances. But for tubes, I'd be looking for 100W+, you'll need something that can use 4 KT88/6550 tubes at a minimum. High power tubes are pricey proposition when you want low distortion, (good trannies) so you might need to shop used.
I liked the Cayin A100-T 100W integrated when I heard it with Quad 2805. $3500 retail.
Audio Research VSi60 uses four of the new, very powerful Tung Sol KT120 tubes, and quality iron. They brag about low impedance ability. I heard it 4 years ago on Wilson Sophia2 at RMAF, sounded very nice indeed. The KT120 is building a great reputation for sounding very good, and making a lot of power. Audio research has switched from Svetlana 6550 winged C to KT120 for their one power output tube used on all new products. It is made by New Sensor, an American owned company in Russia. All of their tube brands are reliable and consistent. You'd have to try this amp to make sure it's a good fit, and it's definitely over your budget, but I think you'd like it.
Edit: The VSi60 is only $4000 retail (2010.) A used one might fit in your budget, and hold resale value extremely well over the years, as all AR gear does.
http://www.stereophile.com/integratedamps/audio_research_vsi60_integrated_amplifier Reviewed with the old style 6550 tubes. New amp have the KT120s.