As you have surmised, everything about the conversion is just fine (headspace, cartridge head support, etc.) except for the reduced thread engagement. If you truly have 12 MM of thread, you should be OK. This is, providing the threads in the receiver and on the barrel are complete and a decent fit. This is not a common occurence on the Savage.
You could replace the bolt head but, be aware, you will also have to replace the firing pin which will then be too long.
So, in order of preference, you may:
1. Machine the recess and deepen the chamber.
2. Replace the bolt head and firing pin
3. Use the barrel as is and worry about it every time you shoot.
There you have it. While I think it is probably safe enough, I would not use it the way it is and would certainly not send it out of the shop that way. GD