Here are my thoughts on my own question.
The thing with a Reaving on that scale is that it would be immensely unpopular with the Bloodname House Leader, and the warriors within, bloodnamed and not. They'd fight a Trial of Refusal for every one (a House Leader who didn't would probably be voted out), and the rules of odds say they'd probably win a few matches.
On the flip side of the issue, a warrior from another Bloodname House has to call the Reaving for each and every bloodright/bloodcount on this House. By doing so, per Clan tradition, the next time that Bloodname House suffers a death, that House suffers a Reaving vote as well. This mechanism ensures that the Reaving process is not taken lightly. It means any Bloodname House that puts itself forward as the Reaving party could be put in serious jeopardy themselves later.
All together, as many as 20 Bloodheritages/Bloodcount from different Bloodname Houses could be lost (or at least in jeopardy) as a result of this (10 from this House, 10 from others). In the eyes of the Bloodname Houses, that may simply be unacceptable to them. Unless they see major political advantage (such as removing the potential votes of an opposing political bloc in the Clan).
The other thing to consider. The book Warriors of Kerensky also tells us that reactivated bloodnames (Reaved Bloodrights brought back online) are generally scorned. So in terms of the prestige of the House as a whole, if you are the House Leader deciding what course of action to support, it might be almost better for you to let it ride, allow those bloodrights to continue. You put your faith on the warriors in question who earn those bloodnames being good enough to fill the void. In the meantime, you get the ball rolling on dramatically increasing the number of Trueborns of that Bloodname House that are birthed in the next several cycles. So that in 20-30 years or so, the problem may be eliminated by increased competition in subsequent generations of warriors. So you stall for time really.
It would be a gamble. The Bloodname House may be flooded with an unpredictable mix of excellent/good/mediocre bloodnamed warriors. You hope they perform well enough that it doesn't bring down the reputation of the House so badly that Trials of Reaving crop up in the next few years to come. Even if Trials of Reaving are called after this generation of warriors earns their bloodnames and die in combat, the hope would be that enough perform well enough that the Trial of Reaving are very few in number. On the scale of a handful or less, rather than 10, when even a Propagation that brings many of them back in years to come may or may not happen, and it can be reliably predicted that those reactivated Bloodrights will be scorned by many.
So there are some additional thoughts to consider. I'd still love to know what course people think this would take.