I'd go with a small inverter. I have a 300 watt one from Wally World that has served me well for many years. I run my laptop, an external hard drive, small sound system, phone and other small battery chargers off of it. You've probably already got a deep cycle battery in your rig, no need to use a different battery.
My concern with a jump start unit would be the fact that they most likely have small starting batteries in them, not deep cycle. Using a starting battery for deep cycle type use will shorten its life. Besides that, they are small. I believe they don't have more than about 35ah storage capacity, and many less than that. Assuming you have a 35ah model, if you draw 3 amps from it for 6 hours you're already down below 50% state of charge, the point at which you should stop drawing from a deep cycle battery if you want it to last awhile. If it's a starting battery, it's not going to tolerate that for too long.