Jack,

Save yourself some trouble and spec VII filled and capped.
Gives the added benefit of protecting from solder flow to opposite side during manufacture and the process requires all vias to be properly filled.
My experience with other fill methods has never yielded acceptable results: either ended up with about 10% of vias not fully filled or with material seepage resulting in manufacturing issues due to the impact on the paste application process.
Going from V to VII will cost slightly more (3-4% here) but that is insignificant in comparison to the costs of failures of assembled product.

Hth,
Dave