yeah twoc/twocced/twoccing is a legit acronym. I realised that the supposed acronym for nonce is "Not on Normal Communal Exercise" rather than "Experience" which makes more sense in the prison context. It can be hard to be sure of word's origin, but in these cases:

• On TWOC, the police actually charge people with "taking without owner's consent". You can find the source of the words in the relevant Act.
• On Nonce, I don't think anyone has ever heard anyone refer to someone as "not on normal communal exercise" - it's an awkward phrase - why is it referring specifically to exercise rather than something more general - "Not in Communal Accommodation" - NICA? "Isolated for own safety" - IFOS? It stretches believability in the supposed source phrase in a way that TWOC doesn't. The earliest attestation of the theory I could find is also from 2012 but the word has been around longer.