Jack,

Further disclosure of my application of VII vias:

I specify only VII non-conductively filled in designs where I want to increase the thermal performance or achieve increased component density. They allow for via in pad design without sacrificing manufacturability. Thermally I would connect these to as much copper as possible with as many vias as possible.

In my present gig this fits well with our product volumes and margins. The fabricators that I deal with steered me away from conductively filled VII due to the associated cost delta. If you hunt around you can find a lot of information on the thermal impact of vias: conductively filled are certainly more effective than non-conductively filled, but in general the thermal dissipation you get from vias is minimal compared to other solutions.

Any type of thermal dissipation at the package is an order of magnitude better than what you will gain from vias.
Do you know how much heat you must dissipate? I consider thermal vias as providing margin but not as a complete solution by themselves.
Is there any opportunity to specify a thermal solution on the top side of the design? There are some epoxies such as 2850FT that work well.
What are your volumes and margins? Perhaps conductively filled VII will work for you.

All the best, sounds like you've got a challenging one cookin'.

Dave