Reviewing the OP, it does seem that since the errors were "all at the same time and with the same amount." as if we have been looking at an FMC error all along and nothing to do with the IRUs?
I am also puzzled by underfire post#4 "BTW, there is a mechanism for the pilot to update the IRU manually with a GPS coordinate." - this is new to me, since in my day, once aligned, the IRU did not have a 'position' to update, and 'position' was purely an FMC function. Have things changed?
Have they changed?
Very much yes!
Take a look at the spec for a 10 year old IRS:
http://www51.honeywell.com/aero/comm..._Micro_IRS.pdf