Here are my thoughts (always dangerous LOL). We don't necessarily need a 'large capacity' battery, but we do require a battery of sufficient C-rating. Almost any low cost RC Lipo pack these will easily handle the current requirements. Just using this $26 example, 5000maH capacity rated at 20C yields 100A. That's C-continuous so 8-10A wont even tickle it. At a load of 2v * 10A = 20 watt-hr, this pack would yield 1.8 hrs continuous running less the usual losses. The issue is the nominal voltage of Lipo chemistry: 3.7v/cell is a mismatch to ~2.0V glow plug. So that entails some kind of step down voltage regulator(s) that can accept this elevated input voltage, and deliver at ~2V and be rated for at least 2A (although I've read that glow plugs can draw 4A+ in certain conditions so best to have more headroom).
Older gen lead acid, NiCD & NiMH have a closer match to glow plug voltage levels but significantly lower C-rating. So you needed much bigger capacity in order to deliver the total amps. I've seen some glow plug driver circuits intended for airborne RC using lightweight rechargeable packs, but I don't have the ability or desire to make my own boards. So that's why I'll likely go down the path of 5 el-cheapo regulators, one dedicated to each plug. Turning them on & off like you mentioned via RC TX at some defined throttle position should not be too difficult, but I suspect a switching do-dad is required which I'm drawing a blank right now. Its used in robots a lot for larger for controlling larger amp draw devices but not as common in conventional RC.
Lets stay connected, maybe there are synergies to our applications. I've still got inventory of NiMH round cells so that might be an option for me too.