I imagine that given that the restoration in that thread dates back to 2010, it pre-dates the regulations restricting the sale for domestic use of dichloromethane, ('DCM) so paint strippers on sale back then such as Nitromors would have contained DCM, which will strip just about anything. (The present formulation is DCM free and nothing like as effective).
It's still permissible to use DCM based strippers under controlled conditions by trained staff in an industrial setting, but not for domestic use. (It's also used quite extensively for graffiti removal). In the UK, the two main DCM products are 'Paramose', and 'Langlow's Stripaway Pro'. Surprisingly perhaps, the latter can be bought on Amazon in the UK by the general public, but formulations that contain DCM are not sold by DIY stores and the like. Painstrippers that don't contain DCM are nothing like as effective.
The risks in using DCM aren't simply theoretical or as some would deride as 'elf 'n safety gone mad' but are very real. A lot of fatalities have arisen through lack of precautions or an understanding of the dangers to health, as a result of which restrictions apply throughout Europe and progressively elsewhere such as the States, and in Australia, as outlined here:
http://www.worksafe.vic.gov.au/pages...ride-in-a-tank
And here:
http://media.mofo.com/files/uploads/...t-Stripper.pdf
So it's more than likely Peter that whatever stripper you've tried on your Sobelette doesn't contain DCM and hence, isn't effective. You might like to explore whether or not you are able to obtain DCM stripper in Oz, and 'ride at your own risk'.
Given the age of the radio, I'd have thought that it would have been sprayed with nitro-cellulose paint, but if paint thinners have no effect on it, it may have been electrostatically powder coated, and baked on. I'm not sure when that process became widely adopted. (There was also 'stove enamelling' baked onto metal items and maybe Bakelite would also have stood that process?)
Good luck with it.