Can I series windings of separate transformers to increase the voltage rating of the whole?
I think it will work fine if they're connected properly (if they share voltage unevenly the one that gets more voltage will begin to saturate and the voltage across it will be limited). 

However the transformers may not be sufficiently rated to be safe on 600VAC, so isolation and creepage distances may not be good enough to meet requirements. At least they're split-bobbin type which is inherently pretty good for isolation. 

Since 600VAC is a common industrial voltage in Canada, there are a lot of control transformers available that will step down from 600VAC to 120VAC or 240VAC. I'd suggest using two of those transformers (600:120-> 120:600 or 600:240 -> 240:600) to get what you want. 

For example, a Hammond B356633 is a 50VA 600VAC:120VAC transformer.