I'd put the battery somewhere in back, like hanging off your seat. You can run the wires up your shirt and down your sleeves... they have very small plugs...
On my motorcycle, I have the wires coming out from under the seat, and plug into a front jacket pocket of my heated jacket liner.
The jacket has built in plugs for gloves and pants liner. And yes, I do unplug my jacket when I get on and off the bike. No biggie.
Email John at info@warmnsafe.com <info@warmnsafe.com>
He's got some really good ideas.
Mary