RWY TRANSGRESS. CLRNC CONFUSION.

Narrative

AFTER LNDG; ON RWY 6 AND CLRING AT RWY 15L; GND CLRED US TO TAXI TO RAMP. WE ADVISED FBO WAS LONG ISLAND JET CTR. GND SAID TAXI TO LONG ISLAND JET CTR PAST BASE OF THE CTL TWR. LAST TIME THERE; WAS OCT/XX/94 AND JET CTR WAS LOCATED AS INDICATED ON MAP. UNBEKNOWNST TO US THEY HAD JUST MOVED (2 MONTHS PREVIOUS) TO OLD KC AVIATION LOCATION. KC AVIATION SIGN STILL OUT TOO! WE PROCEEDED TO TAXI AS DEPICTED AND JUST AS WE APCHED HOLD LINE AT RWYS 10 AND 6 I SMELLED A RAT; AND ASKED MY COPLT WHO WAS IN L SEAT THIS LEG TO STOP AND HOLD SHORT. HE HESITATED MOMENTARILY AND THEN STOPPED WITH AT LEAST NOSEWHEEL PAST HOLD LINE; BUT BEFORE WE ENTERED RWY 10 (RWY 6 ACTIVE). I CALLED GND WHO RESPONDED WE WENT PAST FBO AND THEY HAD TOLD US TO GO PAST BASE OF TWR. WE REMINDED THEM OF OLD KC AVIATION SIGN. THEY SAID YEAH IT SHOULD HAVE BEEN CHANGED WHEN FBO MOVED. WHILE THIS CONVERSATION TOOK PLACE; TWR LANDED AN ACFT ON RWY 6; SO APPARENTLY THEY DID NOT DEEM OUR POS A HAZARD TO RWY 6. GND THEN RECLRED US TO TURN R ON RWY 10 AND THEN 1ST R TXWY TO RAMP. THE REASON I SENSED A PROB WAS I THOUGHT GND SHOULD NOT CLR US BACK ACROSS THE ACTIVE RWY AFTER SUCH A LONG TAXI (IT JUST DIDN'T 'SEEM' RIGHT). ALSO OUR TCASII WAS GIVING ALERT APCHING TFC ABOVE US WHILE OPERATING IN THE GND MODE.