I run a blackline rig, based around an old 2401A pack. I would not think of plugging it into anything less than a 4kW motor driven generator if I was going to consider taking it away from mains power.
The monentary current inrush of the pack just after a full dump. I have tried to measure, and the fastest my analog meter could measure is something like 65A.
The smaller pack would have a smaller inrush, but it would take a hefty invertor to not pop and shut down due to it perceiving a massive overload.
I suspect the sine wave rumour for the balckline might be based around the inductive kick that the fan motors in the heads would present on a modified sine wave supply.
Speedotron is not the sexiest product, but mne shows evidence of taking a kicking in its past life and it keeps on ticking. Do power it up every few months to keep the capacitors healthy.
For on location away from AC work I have a gaggle of older pack and head flash units that I power from gelled lead acid batteries, of the sort usually meant to power UPS and golf carts. The packs might have been designed to work off of wet cells or nicads, but AGM technology with the right charger works them just fine.
The Metz 60 series, Norman B200, and old Braun rigs can do the equivalent of 200w/s or at least be close, and will fill a medium softbox just fine for most on location MF portrait work.