Compiling old packages with outdated libraries for modern distros for preservation and archival purposes

I want to compile old (2005-2012) commits of an app, the app in question uses outdated libraries that no longer exist in modern distros, for example Qt3/Qt4 and ancient OpenSSL. I was successfully able to compile the app under Ubuntu 6.06 and 8.04, but due to missing libraries it would obviously not run on modern distros. My first thought was to compile the binaries statically, but I failed since I would need to statically rebuild the libraries too. I want to compile the app for preservation and archival purposes, and I want it to run out of the box on modern distros, shipping it in something like AppImage maybe? Is statically compiling the dependencies the best way? Or is there a better way?