I owned a couple Profoto 600b kits and replaced the battery with an Amazon lead battery, it’s an easy project and was about $35. Look up the battery then see if you can DIY.
I measured an Einstein e640 to have a cycle surge draw of just over 1000W with the modeling light and power cranked all the way up. With that said I have used it with a Jackery battery and it was fine. Not sure which model the battery was, but it had multiple AC outlets.
Which type of vagabond are you using? There’s aftersales replacement lead acid batteries for the vagabond II battery. Also you can use the alligator clip adapter to connect to a regular lead acid battery.
For the vagabond lithium extreme they don’t service nor sell replacement batteries anymore.
You could buy the vagabond mini. Paul c buff now has free shipping for order more than a 300 dollars the mini is less than 400.
pCB still sells mini batteries and there’s a lot of those batteries floating around in eBay