Robert, excellent parallel about interest in Lenin and Stalin vs NII and his family. We can see today line to Lenin mausoleum, just to see Lenin's corps (how disgusting for my taste). People in general, like to see conforming attractions with their life style and level of education. For example, folks who visiting France usually go to Versailles and only few extend to Château Vaux le Vicomte and Fontainebleau (last one my favorite, I like it much much more than Versailles).
Sian, I would agree with Robert about it, in Yekaterinburg not much attractions, we don't have there seven-eleven and Century theater - to amuse locals, so people go to religious gathering, regardless what this all about (please don't kick me severely for this one, my sister lives in Yekaterinburg).
sckkr, super idea, one problem to get approval from Tsarskoye Selo GMZ - title owner of the building, I seriously doubt who ever will be decision maker, will pass it through like that, because in this case exact amount of restoration will be available for public with all consequences.