Once again, I've managed to tinker through the problem (but not for too long as the original question and this answer supposes it to be :). I've been through almost a month researching the solution for the problem, and I'll leave it documented here just in case anyone happens to bump at the same problem.
Actually, the loopback interface is really what I knew it to be: an address assigned to a dummy, always up interface on a machine. The connectivity problem between the remote GRE router and my router was due to another problem: GRE keep-alive packets.
It turned out that the remote Cisco router was actually sending me odd GRE-encapsulated packets through the tunnel. These packets encapsulated another GRE packet, and these, on the other hand, carried a protocol number of zero. A quick browse indicated that these packets are GRE keep-alive packets, which are send periodically (in my case, every 10 seconds almost exactly) and, if properly deencapsulated and rerouted by the peer, should be echoed back to the sender, since the innermost destination address contained the sender's source address.
The fact is that the Linux kernel did not properly feed the deencapsulated keep-alive packet again into the routing chain. If it did, the packet would be rerouted back to the sender without further complications. Instead, it delivered the packet to userspace, so that it was possible to write a simple program that listened to such packets in raw mode, and echoed them back to the sender. Running this program and echoing back a couple of packets to the Cisco router, the GRE tunnel went 'up' on the remote side, the PIM routers exchanged hellos and I finally could listen to the multicast traffic that I expected to listen to.
I've learned a lot from this experience, specially the part that, when messing with obscure protocols (or, at least, obscure protocol features), you can't simply count at all on peer-knowledge. No single network analyst on the remote side could help me in any aspect in this regard, probably because this behavior was undocumented.
One way is by implementing a smart card solution. Probably not what you are looking for due to the cost and pain threshold, but many smart cards are actually just that (hardware-based certificates with strong private key protection), and the Remote Desktop integration is seamless.
Best Answer
IPSEC is not the tool for this. You need to use a firewall of some kind: Either the built-in Windows firewall or one positioned elsewhere on your network.
You may want to consider using IPSEC to encrypt & authenticate the RDP traffic in addition to a firewall to restrict access to the RDP port, but these are separate considerations from a security standpoint.
Note that you can effectively use IPSEC to block access to RDP (simply require IPSEC encryption/authentication on all RDP traffic, and anyone trying to talk without encryption/authentication won't get through), but this is a side effect and isn't the most correct approach to restricting access. It also means more work for your server (it's going to try to negotiate IPSEC for each connection attempt, rather than simply refusing the attempt if you use a standard firewall to restrict access to the port).