In general, 9V batteries are not good for starting the Estes Solar Starters (unsure about the newer "energetic" starters). You need a good-brand, very fresh battery, and even still it often may take several seconds to ignite. It would seem you should have room in that box for a better battery situation. Running two 9V batteries in parallel doesn't sound like a good idea to me.
Some folks in the past talked about using rechargeable Lithium 9V batteries in their 9V controllers... those should have a lot more juice, but you will need to have a compatible charger for it. Some of them come packaged with charger, e.g.:
AmazonSmile: EBL 4-Pack 9V Batteries Li-ion 9 Volt Rechargeable Batteries with 840 9V Battery Charger. 600 mAh is not a lot, though, you'll want to recharge before each launch and always have spares.
Any modest LED running off <50 mA will be safe.