Electronic – In an isolation transformer, to what is the electrostatic shield winding attached

I think what you did was close, but I wouldn't leave the whole chassis floating. I'm assuming this isolation transformer comes with a standard 3 prong outlet for the output side. Just disconnect the ground connection on this outlet, but continue to let the input side ground be connected to the chassis.

Generally you want as little as possible floating at some arbitrary voltage. There will be plenty of other things around at the normal ground potential, so the chassis of the transformer isn't going to make anything worse.

I agree with Dave in that I don't understand why isolation transformers come with the grounds connected. I got one that way too many years ago, but didn't expect it. I actually blew out a fuse before realizing that the grounds were connected together inside the box. I don't know what they think isolation means, but different from what I had assumed.

By the way, beware of inrush currents on a 500 W isolation transformer. All the ones I've seen are toroidal cores. These can retain residual magnetism depending on what part of the power cycle they were turned off at. If this happened to be at one peak and you turn it on next time near the other peak, there will be a very large inrush. I once blew a 30 A breaker with such a transformer, even though I had switched it on a number of times previously on the same circuit. Unfortunately this was on a weekend and the breaker was in a different locked room. Argh. Often you want to adjust the voltage anyway when you're debugging power circuits where you want isolation. In that case, put the variac before the isolation transformer instead of after it. If you bring the variac voltage up and down with the knob, there won't be much inrush.

The point of a isolation transformer is to break any common mode connection to the rest of the world. This therefore allows one connection to the rest of the world that won't draw any current. Usually you try to not have any such connection, so that a accidental connection (you touching a live wire with one hand while grabbing a metal drain pipe with the other, for example) is the first connection and therefore safe.

A common mistake people make when using a isolation tranformer is to forget that connecting a oscilloscope usually means connection some point to real earth ground. That by itself is OK since it is only a single connection. However, now the circuit is no longer isolated and significant current can flow between some part of the circuit and a metal pipe, for example.