An extremely interesting question.
I don't think I know enough about the different methods to say which one is best but I know google design have some great guidelines on design and animations etc. I had a look for a submit/spinner section but couldn't find one - maybe you can.
Might I suggest an alternative though - replace the text with other text. E.g. Replace Submit with Submitting...and then the dots on Submitting... are animated, similar use of wording for processing etc.
@Gatesunder brings up an interesting point which I've seen on a number of websites. The idea of making the whole page more opaque with a single spinner in the centre. This would be the most explicit method, which also means that the user can't try to interact with the page elsewhere.
As a side note, regardless which kind of method you choose, specifying a minimum time that the spinner is on the page is a good idea - otherwise the spinner might only appear for a split second which doesn't look great because users don't have time to understand what it was that flashed up in the time it takes to blink.
Hope it helped.