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There is an industrial branch taking intense care of the thinning of the ozone layer in the upper atmosphere.
That branch produces foam rubber. Foam rubber gets pretty sticky when heated. Cutting also develops heat and therefor a special oil is required not have the foam clogg up the cutters and cool the blades at the same time.
This oil is silicone oil (also used for implants). It is a perfectly insulating oil and cheap or free to get.
Just visit your local matress factory and ask for a pint or a quart of the oil.
They have tons of it and will be happy to give you a bit of it.
I used to use it in repairing submersible pumps. These use it for cooling similar to transformers, but being submersible, if water leaked into the oil the motor would quickly fail. We would need to replace o-rings and seals and re-fill.
We bought our oil from a local industrial oil supplier, but minimum quantity was a 50 gal. drum. Look for someone who repairs submersible sewage pumps. They probably have a drum handy.
How big is this UPS? I'm not sure I've seen one big enough to warrant an oil filled transformer.