My apologies to Jack for not being able to propose a suitable alternate to Type VII but have yet to come across anything close for less cost.

Virtually all of the designs I've specified Type VII vias on are dense double sided assemblies. The cost delta I stated is based upon ~5K yearly volume.

Before moving to Type VII vias I had previously specified several other methods:
1. Standard via in pad which required inspection and added manufacturing step to ensure proper paste deposition was achieved on the secondary processed side.
2. Tented vias. Frowned upon by IPC specs and not suitable for the majority of the designs we do, didn't work anyways. 
3. Soldermask plugging. Our fabricators essentially told us they could not guarantee 100% plugging stating the soldermask process is amongst the hardest to control. At times we would get to the point with a single fabricator where we had minimal voiding and just a few areas requiring solder bulge removal prior to secondary paste, but we found this varied from order to order. A common problem is soldermask "bumps" at the filled vias. Further complicating the issue was the fact that designs were often moved from fab shop to fab shop essentially eliminating any progress we hade made. 
Note there was added cost when we specified soldermask plugged vias however I cannot recall what the delta was.
4. Peelable Soldermask. Another secondary / additional cost fab process, this worked well for assemblies with only a few areas requiring thermal via in pad. Of course the mask needed to be removed and cleaned prior to secondary paste.

It's really important to consider the overall cost of the product. Saving 5% on bare PCB cost doesn't make sense if assembly processing costs 10% more. Specifying by design a process that may (or may not) result in field product failure is also a terrible choice.
Unfortunately the bean counters always focus on individual piece cost and often a company will need to make the mistake once or twice before the correct decision is made, if they are fortunate enough to survive the bad decisions.

Further, properly epoxy filled and planarized vias have better thermal characteristics than what can be achieved using soldermask.

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