DC Breaker tripping

Sadly, it looks like the sleeping inverter can't awaken fast enough to take up the load. Have you tried leaving both inverters ON and not having one sleep thru light loads ?  

MicroAir EasyStart has a compressor start delay.  When outside unit contactor engages only the outside unit's fan initially comes on.  About three to four seconds later the EasyStart begins its compressor startup sequence.  The initial fan activation should be enough to take inverter out of sleep mode.  Sleep mode pulses on inverter every so often to see if there is a load (>5-12 watts) which is detected to cause inverter to remain on.  Some inverter models allow you to set the length of sleep period between wakeups.  Similar situation applies to inverter-generator in ECO mode allowing time for engine to rev up to higher rpm to support heavier load.  Wiring install of softstarter must leave fan directly on contactor full AC voltage so it doesn't go through softstarter delay.

I have an EasyStart 368 on my 4 ton central.  It has Copeland Scroll compressor which have very high startup surge.  Original factory stock it was 200 amp for 400 msecs. With EasyStart 368 startup surge dropped to 77 amps.  My run current is about 14 amps @ 240vac on compressor with PF of around 0.86 and SEER 15 rating.  The SEER efficiency of particular A/C will have some impact on run current and required HP motor.  Some manufacturers' games are played to get better looking SEER rating but having a large condenser coil size is the best way to ensure a good efficiency.

EasyStart, and other similiar units, are not just voltage ramp softstarters.  They are softstarters with a startup time engaged startup booster capacitor.  The large startup cap gives extra rotational torque during startup.  The startup (auxilary) winding with extra cap and run windings are are both voltage ramped with triac (like a light dimmer).  There is a relay that bypasses the triac after startup to avoid power dissipation heating on the triac.  The units are microprocessor controlled and go through a five cycle training process when first installed to search for best startup voltage ramp rate.  Training should be done on good grid power if possible to avoid effects from inverter (or generator) overloading during initial training cycles.

The above chart is fairly accurate.  It does not address power factor.  I would change the column heading 'Runnng kW' to 'Running KVA'.  Typical PF for compressor is 0.7 to 0.9 depending on compressor load based on environmental conditions.  Higher load has higher power factor, lower load has lower PF.  This is normal induction motor operation.  Hot outside, high inside humidity, and high inside temp is heaviest load on compressor. It takes a lot of btu's to remove inside humidity so once inside humidity and temp drops the compressor load drops by 30-50%.

Poor power factor increases peak currents which increases inverter and cabling losses but true power is what battery sees.

Starting kW is not accurate on above chart (and inverters are rated for kVA, not kW's).  A/C compressor startup is extremely inductive with PF less then 0.4, so expressing startup in kW is not a good representation.  Its the startup peak current and its length of time that caves the inverter.  Typical startup length is about 400 msecs.  Any moderate slumping of AC voltage during startup will just make the startup period last a bit longer.  The important inverter parameter is how much surge current it can tolerate for up to 1 second.