From the live video delivery, this is definitely above my expertise, though it sounds like a fun problem to have. Suffering from success and all that.
The only bit I can contribute is automated deployment is your friend. Many providers will allow very easy to use scripted deployment. I don't know what kind of computer power you need to push, but a VPS with a Gb (in theory) pipe is very cheap, and if you need more more powerful VPS or bare metal a lot of providers allow hourly billing, some even hourly billing for bare metal if you need a lot of compute with it- some providers will not take kindly to you pounding a shared compute instance at 100% CPU. What you should look into do is automated deployment...may k8s, maybe something else. Before you start a stream that might have that many viewers, you can just deploy like 40 instances. You don't even have to worry about bandwidth with most providers since you're just running a short time. When your stream is over, all of the instances are destroyed and the billing is stopped to the nearest hour.

You can seriously do what you need for a couple hours for a few bucks if you don't need a bunch of compute, more if you need compute but still very reasonable. The non-compute heavy go 1Gb/s connections as low as not even a whole cent an hour, and you can distribute this across multiple providers to give more geographic locations.
The one caution I would give with this method is before you invest time in making a platform work for your setup is to actually grab an instance manually and benchmark the connection. Some are 1Gb/s, but will throttle to less during peak times, so test over time too. Know what you are dealing with and how many instances you need.