As someone who has flown the Atlantic in pre GPS days, and who regularly managed to make my coasting fix (NDB or VOR) without any undue concerns, what precisely is the problem you are alluding to?
Might I suggest that if your GPS or IRS is not functioning as perhaps it should in this modern day and age, that you switch it off and go back to basics....assuming that they teach these nowadays.
I still fly all of the ponds, but still use basics as a back up to the modern stuff. Given the excellent wind/temp reporting that they now have, I manage to get within plus or minus 40 miles of the GPS displayed position. Never quite sure though whether it is me or him which has miscalculated!
Whichever way you look at it, and assuming that all is done correctly, eventually you will start to hear VHF voices on the frequencies and in the languages that you hoped for!