I'll trade you for a 30D36R.
MEPs will generally do 1.5X their rated output for brief periods.
1.5 X 2kW is only 3kW.
3.6kW is pushing it. The 30D36R might do the job.
I just finished a 10 day camping trip with the Pow'r Gard in the bed of the truck pulling a 32 ft travel trailer. I have the camper wired through the hitch for 120 vac and the gen worked flawlessly powering the a/c (and the rest of the 30a camper) whether driving or pulled over for the night in the truck stop. great on fuel, too. Surprisingly low noise in the cab with the windows up and a/c on driving on the interstate. One advantage of the Pow'r Gard is that they use a super sized winding on one leg of the 120vac and they are rated for the full output on one circuit. All 120vac plugs are on the same circuit. a nice feature for the 30 amp camper requirement.
As for the 531A, a standard 13,500 btu roof unit is just too much, period. Starting the compressor motor is an issue. The little L40 Yanmar is not oversized beyond consumer ratings at 4hp engine 2kw gen. Recommend swapping it out for a bigger unit. An MEP 016b, e, or 701A will run two roof airs at once, pushing 4kw. A 016D with the L70 Yanmar engine would be nice too. The 531 just does not have enough rotor mass to do it. There is a you tube video of one running a 10,000 btu window a/c. BTW my old inefficient 1985 13,500 roof unit draws about 1650 watts under steady state high outside temp conditions.
If it is the engine that is dying then I have some suggestions as it is not tuned for peak response. I have developed some tricks to effectively remove the power spring which makes the unit ultra responsive to load. Works on Pow'r gard and the L70 and L100 Yanmars.
Various engine sizes for reference
L40 Yanmar in 531= 199cc, 4hp
L70 Yanmar in 016D = 290cc, 6hp
WRDI Fuji in Pow'r Gard = 270cc, maybe 5hp?? (but noticeably quieter and weaker than the L70)
L100 Yanmar in 016E = 406cc, 10hp
106B Onan in 016B and 701A = 603cc, 11hp and 8hp high temp and altitude.