A 3 ton air conditioner is 36K btu. The 60 Kbtu number on label appears to be for gas heater.
Startup surge current can be, and usually is, greater than locked rotor current number on compressor as the number on compressor label is for lowest spec'd AC voltage so branch circuit breaker amperage can be set to ensure locked rotor trip at lowest AC voltage.. You likely have over 100 amp startup surge current.
My 4 ton (48k btu) Copeland compressor has labelled 109 amps LRA. Actual startup surge measured 198 amps for 400 msecs at 240vac with accurate closed loop hall effect sensor. Cheap clip-on ampmeters with surge feature often show lower surge numbers due to too much time averaging. Actual startup surge amps is dependent on grid voltage, wiring gauge and run length from breaker box to compressor.
I installed a capacitor boost / softstarter device, MicroAir Easy Start 368, which brought the startup surge down from 198 amps to 78 amps. I run my unit on 11 kW continuous low frequency inverter that has 124 amp surge capability for 3 seconds. Battery capacity must be capable of the large 48vdc surge current of 600-800 amps.