Any problems with "floating" an oscilloscope?
When we needed to do something like that where I worked many years ago, when testing power controllers that had a direct mains connection (no transformer) under load with a scope I specified a high-power isolation transformer in an "earth free" test area. The setup cost a lot of money, but was necessary for safety reasons, and worked very well.

People sometimes remove the scope ground connection in those circumstances, but it isn't a good idea.

In your case, I'd use an isolation transformer and an earth-free area.