(BBS01b) I had a right struggle mounting my battery - the only place I could put it was the pannier (I needed my folding bike to fold), but that was too small (by a couple of cms) - so I drilled some holes into a piece of pallet wood and nut and bolted it through with washers and metal plates (the type you use to join chipboard with, the flat ones with four pre-drilled holes, about 60mm long and about 20mm wide. They're underneath the plank, gripping the pannier rack), like this:
The mount provided, looks as though you could secure it to a plank of wood on a front or rear pannier, just make sure you measure the pannier carefully - you want it to fit your bike, and looking at your seatpost area... there's not a lot of room - you'll have to take off the rear reflector and/or light. The six holes in the plastic part of the mount: if it were me, I'd consider drilling three holes into two narrow but thickish (but not so thick that they touch the underside of the battery, when the battery is attached to the mount) lengths of wood or strong plastic or nylon, and then add washers on top of that wood or strong plastic, before putting the bolts through that mount - that'd spare the mount plastic... but it might not be necessary, if the mount is made from strong plastic, which it might not be. Then underneath the plank: the bolts would go through the wood, past the pannier rungs, then the metal plates (which would cling to parts of the pannier rack rungs, after you tighten the nuts underneath), then washer (these help get your nuts onto bolts extremely tight and secure), then a nut (or wingnut, if there is room underneath, for convenience).
There may be more room on your bike, for a front pannier?
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A quick trip to the hardware shop (Covid concerns permitting), is required - or a spot of ebay shopping for (hopefully cheap) bolts, buts, washers and plates of the right size. They tend to be cheaper at hardware shops and Poundland, but ebay is Covid-free - they're giving away free Covid in all real shops... wear a KN95 mask, at the very least! And breathe shop Covid air through that KN95 for ten minutes max! ebay is safer.
A piece of plank of wood is practically free... some nuts, bolts and washers will only cost a couple of pounds. Pallet wood never rots, or it rots extremely slowly - that's it's big plus.
Once it's mounted on a plank on a pannier, you could restrict battery movement on the mount, by attaching more wood either side - drill and screw those on if necessary. Or screw the mount onto a 45 degree cut wood wedge, then drill and secure that through the plank - I'd probably opt to keep it in place with wood pieces at front and back, unless you have to move it forwards or backwards to unlock it, or does the battery lift off? If it needs to go forwards or back to after unlocking, just pack it against wood supports, with sponge? And when you need to unlock and remove the battery, remove the sponge? I don't know.
Basically - it's a mechano puzzle. You can't make too many horribly expensive mistakes with pallet wood, washers, nuts, bolts and small metal plates. Just make something sturdy, that you feel confident using. Adjust and change your design as needed. Or throw away the wood plank and start fresh. One way or another - I believe it's a fixable problem.
There's no movement at all with my battery and mount type. Secures fast horizontally or vertically. I had no idea frog batteries jumped about so much! I shouldn't be surprised - they are named after frogs. And they croak faster than larger batteries. Here's my battery - perhaps there's an option to swap yours for something like this? I think it's much more secure for horizontal mounting on a pannier:
If you don't mind my saying: That frame is far too large for you! There's no shame in using a child/teenager-sized bike. They're lighter anyway: more speed and range with a Bafang BBS01b (if it fits)... plus they're cheap secondhand.
Woosh might have more suggestions.