Wow, I didn't even think about Woolwich being at home too, though in my defence I try not to think about them at all.
I don't believe that UEFA would even consider moving one of their precious games for the English third tier competition, which most UEFA-affiliated clubs don't even have, so that's probably out.
I also thought that the PL don't move games for the Carabao, especially ones that have already been moved for TV, although I suppose they may if they come under enough pressure.
So it looks like one team will be shafted - and I think we all know which one it will be...
As far as Man City playing on the Tuesday in the third round, I seem to remember that they actually offered to do so, knowing that they would play their reserves, and at the time I thought that was a stupid precedent to set.
If we are forced to play on Sunday/Tuesday or Thursday/Saturday I think that the club should put out a statement that we will either put out a squad consisting only of players that will not be involved in the Sunday game or withdraw from the competition on the grounds of player welfare.
The only other option I can think of is that they may consider switching one of the games to become an away fixture for the "home" team. Palace v Woolwich would probably not be allowed on the same grounds as both teams being at home (and that wouldn't happen anyway when there's the option to shaft us), so Man U v Spurs at 20:15 on the Wednesday it is.