You are not getting much isolation with an autotransformer. The
primary and secondary are tied together.
It still might solve the problem thought because the connection is on
one if the circuit conductors so the differential toroid in the GFCI
sees the current as being balanced
I still say if you are tripping a GFCI, it is because there is a
circuit from the line conductors and ground, usually a RF suppressor.
It will be designed to pass more if you have a higher current
switcher.
I know there is plenty of "discussion" and plenty of theories but the
guys who actually design them have the opinion I trust.
Isolation transformers are effective in quenching noise (and in some
cases arcs) that can be induced either in the supply side or by the item
being powered. Basically acts as a big choke.
Ever notice what's missing in high frequency switching power supplies?
Big, heavy, iron core transformers.