Untrackable rotating non-repeating IP's per streaming session. How would you do it?

I've had too many assumptions built in to the questions I've been asking, so let me take a step back and ask generally:

What sort of service would you use to anonymize the following?

Establish New IP, fresh browser session, create account on streaming site and logon
Stream for 1-3 hours
logoff
Switch IP's clear cookies, and repeat with new account (never use the old IP again)

Basic requirements are that it must be fast enough to not cause issues with the streaming, must be consistent per session with the IP (IP can't switch mid-session), must not repeat IP's (one IP only per account), must have some sort of kill feature if anonymity is lost, and must provide bulletproof protection making sure their engineers can never see either my home IP or any discernible connection between the accounts. (For instance, if all IPs were clearly tied together somehow) I'm not concerned about the NSA or the law in any way... just can't have the site's engineers pinning TOS issues on me or banning my main account.

Ideally, all they should ever be able to see are IP's from the americas and western europe with as little browser fingerprinting as possible.

Just looking for basic direction to head to start here.

If you needed many IP's daily so that you used each one for one entire session only for a few hours, then switched to the next... and needed to do this many times daily across many vps without ever repeating IP's, what TYPE of approach would you take. There must be a better solution than just buying more and more private proxies. Would you use some tool to auto scrape public lists? Would those be fast enough to to use streaming sites? A dynamic vpn? Some combo?