I don't know what I would choose if I were GMT and Playdek. There's an obvious argument for something from the COIN series, because it's tremendous and much of the work which goes into any of them would make releasing others easier. Also, at least some (maybe all?) have existing rules for AI-controlled players, so the AI programming could be simplified.
A second strong choice would be Thunder Alley, which also enjoys a very good reputation, but has a NASCAR theme which both could draw in players who might not be as keen on GMT's other work and also might put off some of the players of GMT's other games. As a result, I suspect there are some playgroups of GMT fans who have one or two players who really want to try Thunder Alley, but haven't because the theme repels some of their friends.
Third, Sekigahara is lovely and brilliant, with simple enough rules that it would seem more like a normal iPad game than something from the COIN series (especially its more complicated titles). This might be my favorite of their games in sheer physicality; the aesthetic and tactile elements of it are immensely pleasing. So maybe it loses too much in the transition to digital.
Finally, Mr. President looks fantastic and is single-player, so, again, no AI to worry about. I shouldn't think it would be too hard to appeal to those who think they could do a better job than the President--given American political polarization, an awful lot of folks have felt that way within the past year.