However, I'm still concerned about issue of using fake nodes claiming they are someone else (e.g. sending fake OGMs) for sole reason of destroying the mesh. Do you think this is important issue? Can it be somehow reduced?
There are much simpler ways of destroying the mesh, at last locally. e.g, my wife has a cordless telephone which operates in the 2.4GHz band. Pick up the line and wireless in the area dies. That phone quickly got replaced with a DECT phone operating in the USA DECT band, 1.9GHz.
2.4GHz is in the so called ISM band, industrial, scientific and medical. Bluetooth, WiFi, microwave ovens, ZigBee, sometimes radio car keys all work in this band, and all potentially interfere with each other. You are working in a medical environment, so you may find that down by radiography, you can forget WiFi all together?
You really need to tell us your use cases. Do you need a network which has 99.999% uptime? Then dig up the road and lay fibre. Can you live with a best effort network, which will probably die every so often, can easily to DOSed, and performance will probably very depending on day/night, weekday/weekend and the phase of the moon?
Andrew