Nice solution, Ive been looking at probllem for y HXFX this but had not seen the Falken.
in terms of current, the HXFX runs at around 1A, but needs somthing like 2A at start up (I did measure it, but cant remember the exact figures)
Another solution that, i am considering is using bike light battery packs, they will deliver the current, but are only 8.4v so I need to check the function of HXFX at lower voltages. I already use these as bike lights, so know they will deliver 1A for at least 4 hours, and they are cheap! I should add, you will obviosly need to check/swap the polarity! or you will fry somthing!!!
https://www.amazon.co.uk/BSWAN-Rechargeable-13200mAh-HeadLight-Taillight/dp/B07K9RDYSB/ref=sr_1_1?dchild=1&keywords=cree+bike+light+8.4v+battery&qid=1596969062&sr=8-1