Another techniques I've seen is calling RJJJ on HF as soon as going non-radar from PAZN. They can hear you fine from NATES on their primary freq, and all you have to do is fire off a pos report at NIPPI and you're done. The issue here is that while you have an HF backup for CPDLC, it is not your current controlling agency until you get to NIPPI. Splitting hairs, really.
Just don't say 'Heavy' on the radio in Asia an you'll be fine.