So I tried... had two windows open - ie & firefox... at 11:59:59, ie rolled to 11:59:00. Firefox's clocked stopped for about 15 seconds at 11:59:43. When I was able to submit (12:00:00) I had missed any chance.

FWIW, last time they did this the initial time was picked up from the local system. Judging by the time which came up when I first entered the site, they're not doing that anymore, and the time I end up with from Amex is at best about 10 seconds behind actual time (we have accurate clocks here).