Klaus, It would appear that you are looking at your costs in an unrealistic manner. The savings of 10% space is not equal to 10% cost. For multilayer boards, particularly multi-layer with blind or buried vias, your material cost savings are probably closer to 1-2% cost for 10% size reduction. (Unless that small size reduction allows the addition of further multiples within a fabrication panel. Then you might save significantly. It all depends on the size of your boards and how they fit into the fabricators fab panels.)
Materials are typically cheap, the processing costs.
As for your question, there is no simple answer. It would take a lot of details of the design to even start taking educated guesses. Like, number of nets, components, component pitches, trace sizes and spacings, via sizes, board size (as is), etc., etc.. Even at that it would be a guesstimate, only you can know the existing circuit and how much you might expect to save in board real estate.
My very very rough guesstimate, you wouldn't realize a significant size reduction, assuming your design is now quite tightly packed and is forcing this blind/buried consideration. How much addition routing space are you going to realize on any one layer by the removal of a few vias, here and there? If you only need a bit more room in some tight areas like around BGAs (or other very tightly pitched components) , then you might have things work out better with blind/buried vias.
But remember, on a 4 layer board you can't get both regular blind and buried vias in the same design unless your fabricator is doing laser drilled blind vias. I suspect they are not if they are only talking such a small delta in pricing.