That is exactly what I was thinking that they did. To control and limit the inrush surge current, they are letting the inverter voltage drop. Once the inrush current is past, the inverter voltage rises to its normal value and the light is ready to fire. If you look at some of the strobe power packs, they may have two recharge settings, slow and fast. The slow setting restricts the current that is supplied just after the lights fire, but the fast setting doesn't. Balcar has this on some packs and it is normally used if the pack keeps tripping circuit breakers in the 120 volt supply.
You can try different lights with different inverters and most of the time, the worst that will happen is that the inverter will shut down. I think that it is prudent to experiment with cheap strobes that I am not concerned about blowing up. I have some Photogenic monolights (PG4001ML and PG3001ML) that I got cheap on Ebay that I use for this.
Bill
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