This post has gotten too busy and confusing for me.
BCK, me thinks you might be chasing ghost here, and trying to achieve a completely different purpose than what everyone is discussing.
Are you asking this?
When you say isolation transformer, are you referring to one of the SOLA types that you plug into a receptacle, and then plug the oscilloscope into the transformer to isolate the ground on the scope input for bridge type measurements?
If you answer yes, then you are going about it the wrong and very dangerous way. Also if you say yes, throw out everything that has been said here so far because it does not apply. You would violate the scopes warranty, damage it, and likely electrocute the tech’s. You just as well cut the ground pin off the plug cord of the scope, it would work and pose the same dangers as a SOLA isolation transformer.
The right way to approach this is by using one of three methods.
• Differential Measurement System: The most popular and economical solution for floating measurement is the "A minus B" pseudo-differential technique. Most general-purpose dual-trace oscilloscopes have an ADD Mode where the two channels can be electrically subtracted (invert CH 2), giving a display of the difference signal.
• Monolithic Isolation Amplifiers: Connect between the oscilloscope and the circuit-under-test. The signal is coupled across an electro-optical isolation barrier, providing the necessary isolation with superior common mode noise rejection.
• DC Powered Oscilloscope: As the name implies use a dc powered o-scope powered from internal batteries. Recharge when not in use.
Edit:
There is a fourth method. Buy an isolated input scope like a Tektronic THS 700 series and your troubles are history.