Sorry for the double post... it's late and I need to read more closely...
I'm not familiar with formmail. It looks like a remotely hosted service, or a prepackaged mailer that you can just "plug'n'play" onto a website (black box).
My best guess is
Using ASP, PHP, etc... you can fill the hidden field when the page is created, but if the page is kept open for a couple of hours before the "submit" button is clicked, then, well... your time stamp will be off by that amount too.
Getting more creative, you could have your page submit to an intermediate page, that would in turn, add it's own information and then submit onto your formmail...