I'd consider (if you have a 1RU blank or ventilation panel to spare) wiring several such-wired Double-Pole changeover switches (labeled "phase-reverse") onto a panel above, below or otherwise near to the APIs. Then wire a length of balanced-cable-to-XLRs, male and female. This way, you can have them be always in-line with the outputs of the APIs, with no significant added loss of sonic integrity. The front panel thus stays un-drilled ad unmolested, and if you realise that you could use a few for OTHER, similarly "polarity-flip-deficient" pieces of gear, you also can have them available to you.
-Or you can drill holes in the front panel, but I'm always less nervous about drilling in blanks for that sort of stuff.
I do a lot of things that way: the link switch between a pair of LA-2A's, the link switch, preset and battery-reverse switch for an SA-1176 (Urei Stereo adaptor) and other such things that would otherwise necessitate a trip round the back of the rack... just wire them to switches on a spare rack blank, and party on.
Keith