iPhone Thinks IMAP Account is Gmail

Yeah, you can force it do something different by doing manual setup instead of letting it sync the settings. That's what manual setup is for. You don't have to tell the phone it's a gmail account, either, you can choose Other while setting it up.

But I wonder if you understand sync. All the "sync mail" feature does is sync the Settings, not the mail itself in any way. So once each account is set up on your phone, you should be able to turn off the sync mail section entirely and it won't make a difference (unless you are regularly changing your account settings in the computer Mail application). So I don't understand what you mean about "setting up an exception". There is no ongoing exception.

However, sounds like your real issue is:

This is bad because outgoing mail will go out from the iPhone with a @gmail address.

Might want to google on that question, because I'm not sure setting it up as a generic IMAP account will really let you change the sending address anyhow.

Yes, I understand sync, and the sync is the problem. The account is not being set up correctly. In Mail, it's an IMAP account. The iPhone ignores this and makes it a Gmail account.

Okay, you understand sync. So set it up once and you are all fine, and done. It takes about as much time to post here as to set it up manually.