I understand the desire to eliminate inter-board connectors, they are a pain aren't they? However, I predict that with this particular solution, thermal cycles, vibration, etc will cause a lot of field failures. Quite open to failures caused by assembly as well. Perhaps the worst case is you waste a lot of time and have to redesign using conventional techniques. At least I would have a "safe" design prototyped, and ready to go...
There are some manufacturers who make "bendable" FR4 (semi-flex), might be worth reviewing their design guide.