I would tell the CO, that if the $1000 is becoming a burden, they should keep it. Then, I would suggest that they should cut a deal with the scouts (and any other group) that for each month when that group volunteers, $85 will go to the to their treasury.
Is only $85 a night worth it to the committee? It depends. Are there other advantages to getting scouts "front and center" in uniform in public slinging burgers and sausage once a month? Can the scouts serving get a free meal?
Are you just a Pack? Or, Pack + Troop + Crew?
If my crew were sponsored by this CO, I might take them up on it. We'd arrange to have our officers' meeting that night, pass out recruiting flyers, and maybe even flash a slide show of recent activities.
Beyond the charter renewal fee, does your CO provide meeting space/storage? If they do you need to figure that into your calculation. Yes, it's part of their responsibility but that doesn't mean the cost is $0.
Being that it is one Wednesday (which hopefully is not your meeting day?), I'd do the cost/benefit analysis of whether you would make more money for the unit if you kept the profits from the events than the $1,000 annual payment. I'm not saying that means you commit to it, but I would use that as part of my rationale to the CO on why the arrangement doesn't make the most fiscal sense. By the same token, if the expected profits are less than a $1,000, the math then works to your favor on why not to do it. if @Jameson76 's math is close to the real picture, you can find fundraisers that will bring in more than that level of funds with that time investment.