I'd say what you need is a godox 360, or maybe even the 180. I'll speak for the 360, because that's what I have.
In comparison to a speedlight, it's waaay more powerful, even in comparison to the 600 so it will lit large modifiers with no problem. Also, it has a battery that will last for way longer than four AA. Further, it's bare bulb, so it will fill the softbox beautifully, unlike a speedlight. On the down side, it's bulky and heavy, but it's certainly portable and you can even mount it on the hot shoe. I know I do, and I don't even have a professional magnesium body.
In comparison to strobes, it's somewhat less powerful (360ws versus 400ws or 500ws for common portable strobes) but it's way more portable. Try mounting a strobe on your hot shoe!
Back to comparing it with your Canon 600, the Godox doesn't do TTL, it's manual only (albeit with a very easy to use remote power control), but it can do HSS (High Speed Sync) if you use the correct remote triggers, or have it on the hot shoe, so you don't have to worry about sunny days.
I'm attaching three pictures I did with it in the last month (the last one using HSS, since the background is in the sun).