Cisco Released an OpenJRE version of ASDM in the most recent release of the ASDM software ( ASDM 7.12.2 ) on May 29th 2019. You can find that in your Support and downloads section, here is a direct link: https://software.cisco.com/download/home/2795...
I've got the same issue, I can connect using the client to one of my ASAs but noe the other, the one I cannot connect to is a new configuration, but both are running the same ASA version and use the same XML... I've re-checked everything I can think...