Ctrl-Enter might work when the people filling in the forms are familiar with the site and use it often. Otherwise I would stick to Enter. I don't think there's any harm in that, especially when you take your second approach (validate and focus on missing fields). Of course, you also need a “Save”, ”Submit”, … button — don't rely on the shortcut alone.
If your form doesn't have multi-line fields, I see no reason why you should use something different than Enter. People know and expect it.
When you do have multi-line fields, things get more complex. If your form is for entering articles or longer text (such as this answer form), then Enter should start a new line. If it only happens now and then, Enter could save the form. So I guess it depends on the use — as usual.
When you use Enter to save the form, the way to enter a new line is unfortunately not very standardized. Excel in particular makes it quite hard: Alt-Shift-Return or something like that (it's not only hard to type, it's even harder to remember).
But, I would love to see a site where Enter did enter my data even if I'm not in a text entry field. I gets me every time I need to log in: type in user name, TAB, password, then click the ‘Remember me’ checkbox, then hit the Enter key. Bzzzz!