Im happy to hear that you got it worked out on your servers.
The installer/upgrader script has been tested multiple times without error, using 7.5.5 as a base for upgrading to 7.6.1.1. Though, I will take your suggestion and proceed with another fresh install of 7.5.5 on a completely different spec'd server. Then do a vanilla upgrade to 7.6.1, following the exact upgrade steps as listed in the Docs menu tab.
I appreciate you reporting the issue, and I'll try my best to duplicate what you dealt with. As I had not come across your issues at all. Nor have I read about anyone else with those issues.
To better help duplicate this on my end, and prevent it from happening to anyone else in the future, can you copy/paste in to a reply here, your server specs shown in the right-column of your forum Control Panel Dashboard.
Again, thanks for reporting this