Hello and welcome to JustAnswer!
Unless something external is physically blocking the shifter from moving then the problem has to be internal in the transmission. It wouldn't hurt to take a look around the shifter area under the boot and make sure nothing foreign is blocking the shifter from fully moving intermittently.
I don't believe that's your case though, especially if you're having the engine die when letting out on the clutch or it moves in reverse when you have the shifter in neutral. These both indicate internal problems in the trans. The problem sounds more likely to be shift fork and rail related rather than synchronizer issues.
If you don't see anything foreign in the shifter area, which again I don't believe will be your case, then I would recommend returning to the shop that did the transmission work. Since they just rebuilt it then they owe it to you to correct this problem. Almost certainly the trans is going to need to be removed and disassembled again to diagnose and repair it.