> 12V ... 300mA ... 15 minutes

I'd consider a 12V 1200mAh sealed lead. Last ones I bought (from
an alarm wholesaler) were NZ$15 (about US US$9.50). If looked
after they'll last for a long time. A 13.8V charger is pretty simple to
build. They only things to watch are draining to, and leaving at, less
than ~11V and over-charging. Plenty of info on the web about caring
for SLAs

However, you didn't say if there's a weight restriction, maybe an SLA
isn't suitable. I think the smallest available (but perhaps less common
and more expensive than the 1200mAh) is 800mAh

An option is to buy a cordless drill and use its battery. Cordless drills
can be had very cheaply these days. Think of it as a very inexpensive
NiCd pack with a drill thrown in

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