Alright so lets take a serious look at the GDR, remove the idea of a joke unit and say "this is the last unit I will ever make in this game...what does it need to do?" For this unit to be effective, it has to be able to bring tremendous punishment in a very short amount of time to be actually taken seriously. It also does not have the turns to sit back and heal, its got to fight and fight again, or it won't be effective. Considering it is also siphoning off uranium that can be used for nukes, it has to be worth such an investment. So in general, I think we start with giving it a lot of the key abilities of many units in the game.
1) Recuperation: March, Double Heal (from Immortals), Medic II (CS adjusted for the penalty), and heal on kill. The GDR does not stop....until you are dead.
2) City Takedown: City Assault Promotion. This boy brings the pain to cities. A few of these should drop a city in a few rounds if left uncontested.
3) Air Defense: Air Defense 60. Stealth bombers are common at this point, and no matter how strong a GDR is, they will take it down quickly. A high air defense ensures that bombers have to rest while the GDR is bringing the pain.
4) Mobility: High speed, amphibious. Rivers and embarkments don't slow them down. If we want to go all the way with full ocean movement I think that would be cool, but I recognize that's a paradigm shift.
Such a unit will push forward, resisting aircraft, healing heavily as it goes, and bringing a lot of damage quickly to cities. Its a unit that if not accounted for, could actually take out an empire in a matter of turns....exactly the kind of power you need in the last vestiges of the game to give a player a chance to strike at the runaway and actually have a chance to stop them.