Keep in mind that if the back A/C is 13K or even less it doesn't draw 20A so all of the remaining available amps are available to the rest of the house.
i disagree with that statement
5000w generator stators are not wired with a 27amp winding and 14amp winding,even though they have 30 & 20 amp breakers
trying to draw the extra amps thru the winding feeding the house creates extra heat in the generator windings
in fact impossible ..IF the neutrals were brought out separately and not tied as center tap in the generator, which creates two separate outputs with no common neutral for load share the difference in amps
which might be the way this one is wired
i got to dig into that when the weather cools and i have time
should have checked that out earlier, just never though about it
i do know only the hot wire feeding the 30amp main goes thru the load senseing coil for the climate control