Surely this wouldn't take more than 2 weeks: just figure out the install instructions for the old piece of software, rewrite them as a part of a Dockerfile (or similar set of instructions to build an OCI image, there are other options out there, too), setup some basic CI/CD which will execute Docker/Podman/... build command and update any relevant documentation.

I actually recently did that with some legacy software, apart from additional optimizations like clearing yum/dnf cache after installs, it was pretty quick and also easy to do! If you are also in a situation where you need to use EOL software, I don't think there are many other decent options out there, short of trying to reproduce the old runtime on a new OS (as others suggested).

Running the old EOL OS will simply leave you with more vulnerabilities with no fixes in the long term and is generally a really bad idea. How did your security team greenlight that idea? In some orgs out there the devs would be made to stop doing whatever they're doing (outside of critical prod fixes) and would be forced to migrate to something newer before proceeding.