SMA PLT IN IMC MAKES NAV ERROR ALMOST HITS TWR.

Narrative

WE WERE FLYING AN SMA FROM FNT TO TVC VIA FNT DIRECT TO MOP THEN V320 TO TVC. WE STARTED VFR FROM DTW. SNOW SHOWERS MOVED IN VERY RAPIDLY SO I DECIDED TO SHOOT AN ILS TO LAND AT FNT. ON THE GND LANSING FLT SVC ADVISED US THAT THE SNOW WOULD END N OF MOP AND BE VMC. WE DEPARTED IFR EXPECTING TO GO VFR AROUND MOP. WE WERE CLRED TO 4000 FT. I REQUESTED TO STAY AT 3000 FT TO AVOID ANY ICE WHICH MAY HAVE BEEN IN A HIGHER LAYER. WE WERE IMC AT 3000 FT WITH INTERMITTENT GND CONTACT. OUR RTE OF FLT WAS TO DEPART MOP ON V320; WHICH IS R333. HOWEVER; I DEPARTED ON R320 OFF MOP. SAGINAW APCH HANDED US OFF TO ZMP AND ADVISED US THAT CTR WOULD NOT BE ABLE TO SEE US OR TALK TO US FOR AWHILE AND THAT WE SHOULD TRY THEM EVERY 5 MI. THERE WAS NO MENTION OF OUR NAV ERROR AT THAT TIME. WE WERE ABLE TO RELAY THROUGH AN SMA WITH CTR. WE WERE ADVISED TO TRY AGAIN 30 MI S OF TVC. WE CONTINUED ON R320 AT 3000 FT. CTR THEN RELAYED THROUGH AN SMT THAT WE WERE GETTING CLOSE TO A TWR. AT THAT TIME WE WERE ABLE TO ESTABLISH OUR OWN CONTACT WITH CTR. WE ASKED FOR VECTORS AROUND THE TWR. THERE WAS A LONG PAUSE. HIS REPLY WAS; 'YOU MISSED THE TWR BY 1/2 MI.' HAD RADIO CONTACT BEEN ESTABLISHED SOONER OR CTR RELAYED THROUGH THE SMA; WE MAY HAVE BEEN ALERTED TO OUR NAV ERROR SOONER AND BEEN ABLE TO PASS FURTHER FROM THE TWR. I HAVE DISCUSSED THIS FLT AND OCCURRENCE WITH OUR CHIEF FLT INSTRUCTOR. WE REVIEWED THE POSSIBLE REASONS FOR MY ERRORS AND THE PROPER CORRECTIVE ACTION.