PLT OF SMT ACFT AT BHM STARTED INTO POS AND HOLD; BUT REALIZED CLRNC WAS FOR ANOTHER ACFT AND TAXIED ACROSS THE RWY TO THE OTHER SIDE.

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SPECIAL ACFT WAS CLRED TO TAXI TO RWY 24 AT TXWY G. WHILE HOLDING SHORT AT TXWY G; A PARTIALLY BLOCKED POS AND HOLD CLRNC WAS GIVEN FOR RWY 24. TO BE SURE THE CLRNC WAS FOR US; THE FO REPLIED 'POS AND HOLD; RWY 24; ACFT X.' WE PROCEEDED TO TAKE THE RWY. LOOKING OFF TO MY L; AN AIRLINER (POSSIBLY A B747 OR A B757 AND WAS ALSO POSITIONING FOR TKOF. WITH AN ACFT ON FINAL APCH (APPROX 2 MI) AND AN ACR FLT POSITIONING FOR TKOF; THERE WAS OBVIOUSLY MISSED OR BLOCKED XMISSIONS BY THE TWR AND/OR PLTS. FOR THE BEST INTEREST OF SAFETY; WE PROCEEDED TO CROSS THE RWY TO AVOID ANY JETBLAST FROM AIRLINES; OR THE ACFT ON FINAL APCH HAVING TO DO A GAR. AFTER XING THE RWY; I (THE CAPT) NOTIFIED THE TWR AND SAID WE WENT AHEAD AND CROSSED RWY 24; THINKING HE HAD SEEN THE CONFLICT. HE RESPONDED 'I SEE THAT.' IT MAY HAVE APPEARED TO THE TWR THAT WE CROSSED WITHOUT THINKING WE HAD AUTH. BUT POSSIBLY DUE TO RADIO CONGESTION AND HIM WORKING GND AND TWR OPS HE MUST NOT HAVE REALIZED IT. WE THEN; BECAUSE OF THE NARROW TXWY; ASKED FOR A TKOF CLRNC FOR RWY 18. THE TWR ISSUED A CLRNC AND THE INCIDENT WAS OVER. SEVERAL DAYS LATER A PLTDEV/RWY INCURSION RPT WAS FILED AND THE FAA IS INVESTIGATING. I FEEL THAT THERE WAS NUMEROUS BLOCKED RADIO XMISSIONS AND BOTH PLTS AND CTLRS SHOULD HAVE QUERIED EACH OTHER MORE THOROUGHLY. DUE TO HIS HVY WORKLOAD AND OUR ACFT PRIORITY STATUS; THIS INCIDENT MAY HAVE NOT EVER HAPPENED. I THINK OVERALL THE ACTION TAKEN TO EXIT THE RWY IMMEDIATELY WAS IN THE BEST INTEREST OF SAFETY.