Okay went out and took a look. I think you'd be okay as far as the cut-out. The HE2's have a cut-out of 11 1/8" (at least the ones they have at Crutchfield do
) which would only put you 15/16" wider for the cut-out on all sides. You've got a healthy inch at the least all the way around in the interior. I'm not 100% sure though that the mounting flange wouldn't go past the lower dimensions of the box but since it's 5/8" MDF you've got plenty of room to set screws.
You will definately have to trim the ABS lid though, don't think there'd be anyway around that.
HTH.