So has anyone measured how the IFI Audio AC Purifier is supposed to work?

[solderdude]

My question is, is there any device I can get that could lower it down to below 10mVA? Would a UPS with a lithium ion battery work much better?

There will always be some RF creeping in. Every device connected to mains injects some anyway, certainly when they have a switching power supply.
Also the ones on the 'cleaned' side will thus inject RF into the 'cleaned' side, it will just be attenuated when it goes into the mains.
'Measuring' RF is kind of an art form because when not done correctly you can measure the wrong thing.
RF can come in via not really obvious paths in the measurement while when removing the measurement gear it would actually not be there.
Such (cheap) RF meters are somewhat indicative at best.

As long as any RF remains below the detection threshold from audio devices (so you hear nothing weird when on and not playing music) there simply is no need to do anything about it.

UPS designed for PC backup voltages may even generate more crap than mains itself, the type of battery is only important for longevity, temperature range and weight.
A battery-backup UPS that never runs on the battery (always connected to mains) will need to have their batteries replaced every few year or so as the battery is not used anyway.