I've done the display and handling of forms via AJAX before, I've got a write-up on the wiki:
https://docs.moodle.org/dev/User:Mark_Johnson/Mforms_and_AJAX
This was pre-moustache through so I don't know how/if it would integrate. Also note that that guide is based on YUI's io-form module, as Davo says you'll want to use the jQuery equivalents to serialise the form data and do the AJAX calls.
