I don't have the HE-400, but I do have the HE-6, and with those, I've got about 1/4 inch of play left on either side of the headband. With the Mad Dogs I have more than an inch of extra room to extend the headband. You can also gently bend the headband itself to adjust width / clamping force. You should be fine.
Would you say they are any larger than the dog pads? As I said before, for some reason, especially with my left ear, the Dog Pads don't quite fit all the way over my ear, and I get discomfort after listening for a few hours. But it definitely sounds like something I'd like to get. If they have better comfort, that all but seals the deal for me.
Is it the depth or circumference of the Dog Pads that wasn't big enough. If it's the depth, then these should more than cover you. If the opening is just not wide enough, then I'm not really sure that these do anything to fix that (though if that's the case, then you're looking at ESP-950's, HD800, K1000's, and possibly the Stax Lambda's and K701/2's); there's not really that many cans out there with huge openings for the ears.