Of the three songs looking back on a lost relationship, I think WAW is the strongest (and also the one that represents the biggest step forward for Carrie, thematically) and a few weeks ago, that would have been one of the songs I would have seen as a good single for her.
Now, however, I think the release of SYA creates a different impression for the album when compared with the very innovative first three singles. I feel Carrie needs a musically high impact and assertively Country song to re-emphasize that the BA era is intended to take her work to a new level. In that context, I wouldn't see GIG fulfilling that objective (and I'm afraid I'd see DYTAM as the worst choice - not because it's in itself a bad song, but because I see it as rather lightweight, too generic, and really offering nothing to lift Carrie's stylistic range) WAW, as I say, would have been a forward step, but now I see it as rather too slow and and subdued to have enough of the forceful impact I hope for.
So my choice now would be CGAS - one of Carrie's strongest excursions yet into Country Rock, which I feel would reinforce the memorable impact this album era deserves