I think you're asking too much here. The Zoom F8 is probably the cheapest 8 ch. portable solution available.
If you reduce the number of channels you'll have more options. Like the Boss BR-800 or the Zoom H6.
You may be able to find an external audio interface which you can power up from a battery supply and use that along with a laptop or tablet of some sort. Two such interfaces are Focusrite Scarlett 18i8 and Behringer FCA1616, both running from an external 12V DC power supply which can be created easily with batteries. I'm not sure how "portable" this will end up being, but it will be cheaper, provided that you already have a laptop etc to use.