if you need a isolation transformer, dont go for the 220/110 convertor, its a autotransformer, you can check there will be a reading between primary and secondary.
as you heard its centre tapped to be connected as 110/220
you can follow the idea of RCinFLA
or rewind a transformer 240/ 24 V, dont open the primary and make the winding of secondary as the same SWG of the primary and number of turns is 10 times of the secondary you unwind. if you use 240/12v T/F then you can calculate the number of turns. and it will be 20times.
or you can use two 220/12V or 24V transformers connected 24V side together, so input and out puts would be 220/220 and will give a good isolation.