I should have prefaced my comment by saying that I’ve never assembled BGA devices in this manner so take that into consideration. I’m just throwing ideas out there for thos who may need to design with a BGA device and can’t reflow solder.
Re - tinted vias: I guess I should have said ‘no plugged vias’. As long as you leave the opposite side clear of soldermask so that you get good heat transfer you should be able to reflow.
The problem with this idea is that you will really need to add some solder through the via. If the part or pads are not absolutely co-planar, then you could have a case where one ball will not solder to the pad when it’s via is heated from the opposite side. Even adding solder at that point may not help.
I would only attempt this with low ball count, course pitch bga devices though.
Steve