These may have just been edge cases but the second issue seemed to simply time out while on the "Wait for the host to be up" task. Jobs ran inside of HostedEngine and the retries expired before it was completed.
I needed to edit line 147, `
retries: 120`, to a higher number so the process would complete and return the expected check result. (For reference, I made it 999 - just arbitrary)
File requiring edit: /usr/share/ansible/roles/ovirt.hosted_engine_setup/tasks/bootstrap_local_vm/05_add_host.yml
I did not run into the space limit on `/tmp` mount again so this _may have_ been from previous attempt just clogging that space up.