reldude, by all means volunteer--- at the time you volunteer, you can ask what they will offer as an alternative. My hunch is that the flight to LAX plus Super Shuttle is what they would offer everyone. Especially this being Christmas Eve, if the LAX flight is still open, I think that would be preferred vs. rebooking the next day.
I myself have been bumped on CO IAH--ONT and routed IAH--LAX like 10 min. later, with a shuttle to ONT. I checked bags to ONT so I had to go there... but other occasions that I've been bumped on a DCA flight and routed to IAD with a taxi voucher to DCA, I can usually use the voucher for a direct taxi home since the fare IAD--DCA is about the same as IAD--home.