Moiraine and Lanfear might very well have burned out or were at least incapable of channeling for some time, so that the Finn could capture them. (although BS's statement about transmigration and stilled channelers seems a bit odd, if Lanfear burned out)

It makes sense that a melting ter'angreal has such a side-effect like burning out. Plus, it would nicely explain the broken bond. It also makes sense that Moiraine wanted to assure with her deeds (especially placing the angreal near the doorway), that the doorway ter'angreal would melt and that Lanfear would burn out, because otherwise - i.e. if Lanfear was still able to immediately return to Randland and kill Rand - nothing was really won.

That Moiraine knew that she would probably lose her ability to channel would also explain better the thoughts in her last PoV about the great sacrifice she makes, because she knew that she probably wouldn't die immediately, but that the Finn would imprison her and Thom & Co. could rescue her.

Finally, I think it would be cool if a young Moiraine without the ageless look is already seen by Rand through the swirling colors to Mat, but of course Rand doesn't realize who this woman is till he meets her in person & cries then (probably in Caemlyn).