Cornish Jack - I wonder if I've read the same incident reports as you mention...there was an incident where a crew misaligned their IRS before departure (finger trouble) and after leaving VHF Navaid coverage their FMS position diverged from the actual sufficient to cause a potential loss of separation (can't remember if it actually resulted in TCAS mid-atlantic or not). Certainlyerrors of the order of around 70nm involved.
Never never never enter MPNS airspace if you suspect that your IRS has not been aligned correctly or your FMS/IRS position information is invalid.
There are guidance notes in UK CAA AIC 33/2000 (see
UK Aeronautical Information Service) for loss of B-RNAV capability enroute - so that might be worth a thought if you suspect that FMS position is having trouble.