Offline HTTPS test?

If you have a Linux machine in your local network (or if not, just set up a VM – or use the provided Docker file to generate a Docker container), you could take a look at testssl.sh – which is a command-line tool to check SSL setups. It's quite flexible, can be adjusted via command-line parameters, scan against any port (not just 443) – and can even generate "machine readable output" (CSV, JSON). Run the script without any parameter (or just pass --help) to get a list of options. Or simply pass it the URL to your server to get a full report, e.g. ./testssl.sh https://example.com/.

Note that the handshake error usually is no issue with the cert, but with incompatible cipher suites or protocols. The output of testssl.sh is quite extensive, and certainly should give you some clues.