Assuming you can't find a DEN/SFO/IAH/ORD reroute (worth investigating, per above suggestions), then the primary considerations are 1. how much does it cost you ($, opportunity) to arrive LHR a day late, 2. how much does it cost you (same) to leave PHX a day early? There is a low chance you would misconnect at LAX, but if cost 1 is significant, then cost 2 could be more appealing.