The user hit the submit button, the "page" doesn't go to the server, but the form's "data"

Yes, I simply misspoke. I was writing my reply too hastily, I think.

The net sum of it all is that the client can't be told to popup a dialog, or do any of a number of things it "can" do, because it's not part of the http protocol.

Precisely. I suppose you've moved past the stage of wanting an actual working solution to your problem, to the stage of wishful hand-waving. Not that I think there's anything wrong with that. In fact, it's usually quite an entertaining activity to engage in. 8^)

it's also not unique to shortcomings of the http protocol

I don't necessarily view this as a "shortcoming" of the protocol. It was originally intended as a simple protocol for, erm, transferring hypertext. All this other stuff (that makes it useable for applications, though not necessarily perfectly suitable) was shoehorned in later. The fact that it doesn't work ideally in all cases should hardly be surprising.

As for a way to create more rich web application interfaces, you might want to look at XUL. It's a Gecko thing, which may be a problem for you, but even still it's pretty neat. Using it for a public-facing site may not be practical, but for internal use it just might be nice.