Hello Sam,
First I would recommend opening a support case for these installation issues as they are a little beyond what can be dealt with, via the forums, in a timely manner....however I can answer your questions...
is there any harm with it trying to rerun the configuration on other nodes that have already been configured?
No, you can rerun instance configuration at anytime. It will go thru the steps of configuring all nodes again, but this is not harmful.
Moving forward we are looking into the ability to check off nodes, where Litespeed is already installed, so they are not include in the re-running of instance configuration.
I'm giong through the logs now to see why, but anything in LiteSpeed that would cause a failover?
Not during an install. To confirm we would need to see the application and system event logs (in EVT format)of the node that failed over, Litespeed installer logs from the node where instance configuration was ran and, if possible, any SQL\windows dump files created on the active node which failed.
Just as an "FYI"...I have seen the error shown in your screenshot before, but I would need to confirm its the same issue first. So, again at this point, please open a support case.
thanks,