All EFIS display systems get their Heading information (Mag or True) from the IRS alone. FMS can not be used as a source as its software level is not high enough (IRUs are Level A, FMC Level C at best).
I've seen the latest Airspace plan for the US & it will still be close to 25 years before the current SRNs are discontinued. Even with the additional signals available when the new series of GPS satellites is finally up, it will still be a single source - arguably single failure - system. NavCanada did a study that cast doubt whether GPS can ever really be used with sufficient repeatable vertical accuracy for CAT I let alone CAT II or III (current GPS approaches have MDAs lower than normal but still well above CAT I (200 ft agl).
Either way we won't be out of a job soon with all the system updates this will entail.