Best way to have a simple http proxy server/tunnel with multiple outbound ips

I have a couple hundred of servers connecting to HTTPS endpoints, and currently each one have a public IP address. I want to tunnel them through a smaller set of standard outgoing IP addresses that I can manage. I don't need filters, authentication, caching or anything. I just need an open port that exits through a specific fixed address.

It would be ideal to start a VM with an arbitrary number of interfaces, and start a service that opens a port for each outgoing interface. I can dynamically generate the configuration if needed.

Everywhere I look, I see squid as the recommended proxy server, but it sounds too much for what I need. Is it the best tool for this job?

I also looked at SSH tunneling, but it gets complicated to establish and maintain tunnels from each server. Ideally, I'd like for applications to simply use an http proxy server when needed.

Are there other options I'm not seeing to achieve this?

Thanks in advance.