Well, for both BA and AA you're allowed one carry-on and one personal item. AA specifically lists a soft-sided garment bag as being equivalent to your carry-on. So I think you may be over your allowance! Of course you could consider consolidating all three suits (plus the extra jacket) in a single garment bag. Would that work? If it were me then I'd probably just pack the suits in a suitcase and then, if necessary, have them pressed when I get home.

In terms of Sunday being hardly peak business travel I would disagree. If I needed to be in the USA for work on Monday then I'd be travelling on Sunday.