I would say more battery.
While a 30C battery might handle a 30C discharge max (for short Spurts), if it is anything like an RC type battery there still will be voltage droop, resistance on the wiring and connections and 15minutes is a good runtime
when using things that hard.
According to my calculations you got about 100Wh total of battery, so it is only about 1C for a 100W load. then you have to include the "ballast" losses, whatever converts for the HID voltages, is going to have 10-20% loss (more power still). It might be a 100W arc bulb but what is the total power consumption when including the ballast?
the Voltage Under Load:
Check your voltages on the battery while under that kind of load. Mabey check for any voltage drops along all pathways, including things like switches. To check along the paths with DMM, just move the other meter "probe" down to different areas of the wires and connection points, while under the large load.
loosly i would say you need about 10+Lbs of battery
of any kind to be doing a 100+W for any ammount of time. at the least i would want about 250wh worth of any battery just generally speaking. Ya wouldnt try to run a 18650 flashlight off a 10400 battery
and that could be parts of the problem.
Parellel more actual capacity in. If your trying to portablise what is run with a car battery, then get going with 1/3 of a car battery not 1/10th.
check any of the losses on the wiring. Check out big fat li-Fe batteries, they can more easily be designed to replace a car battery, and handle loads without drooping better than li-poly RC even. Do a check on your li-poly for total actual capacity, and drain stats.
Other than that, need more specs, and i dont know enough about how the ballast would load the battery, as in be hitting it in spikes? Much more battery would not notice any load spikes as much.
At the least provide:
1) some voltages under load,
2) provide the actual capacity of the battery as tested,
3)tell of the methods used to charge, the inital unloaded voltages and if it is balanced.
4) any kinds of protection that it has,
5) any Pictures of what you got going on. Pictures being the only fun part
6) spec sheet on the Hid ballast, or the actual power consumption specs.