I don't see the GB being "done away with" but I could envsion them letting themselves die off without replacements (20-30 years and they're all gone). They would need to revise some doctrine but they'll have to revise doctrine by then anyway. My speculation follows:
Fifty years from now the doctrine will be that the 1000 years began in 1914 and that rather than the "old light" understanding of two separate Armageddon-like events (one to kick off the 1000 years and one after the 1000 years), there is just one at the end of the 1000 years. They'll also have to change "the rest of the dead didn't come to life until the 1000 years had ended" scripture to literal instead of figurative, since there is obviously no resurrection going on right now.
This will bring up the issue of what to use as a stick without an Armageddon imminent. Here is what it will be: the lake of fire. Anyone who leaves the Borg during the 1000 years has NO HOPE for a resurrection. Anyone who rejects "the good news" during the 1000 years has NO HOPE for a resurrection. ONLY faithful JWs who DIE FAITHFUL during the 1000 years have hope for a resurrection (along with everyone who died prior to 1914).
See? It's all laid out for them. They'll perpetuate the Borg indefinitely with this scenario (or one something like it). How does this relate to the GB? Well, they (along with ALL 144K anointed) will have been resurrected to heaven and ruling from there. On earth, the Watchtower will set up some sort of administrative hierarchy that are "the princes" representing the Borg interests on earth. It will be GB-like, but with less prestige and absolutely no power over the organization, which will be corporate-run in reality.