B767-300 CREW HAD A RWY INCURSION AT LGA WHILE RETURNING TO GATE TO HAVE AN ELECTRICAL ACCESS DOOR CLOSED.

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ELECTRIC SVC PANEL DOOR WAS RPTED OPEN BY ANOTHER ACFT AS WE TAXIED INTO POS AND HOLD ON RWY 13 AT LGA. ARRS LNDG RWY 22. TOLD TWR WE HAD TO RETURN TO GATE AT FAR END OF RWY 13. TWR TOLD US TO TAXI DOWN RWY 13 AND HOLD SHORT OF DOUBLE ALPHA. MY MIND SET WAS TO CROSS RWY 22 (TFC WAS IN SIGHT APPROX 2 MI OUT) THEN LOOK FOR DOUBLE ALPHA. COPLT WAS MAKING A QUICK PA TO LET THE PAX KNOW WE HAD TO RETURN TO THE GATE. TWR STARTED TO SAY HOLD SHORT; THEN MID SENTENCE SAID TO HURRY ACROSS RWY 22 AND TURN R ON TXWY L. TFC WAS STILL APPROX 1 MI OUT. IF YOU LOOK AT THE 10-9 PAGE FOR LGA; DOUBLE ALPHA IS A HARD TURN TO THE R; APPROX 135 DEGS AT THE INTXN OF RWYS 13/22. SPOKE TO THE LGA TWR SUPVR; FIRST TO APOLOGIZE; THEN TO EXPLAIN HOW HARD IT IS TO TURN A WDB ACFT ON SUCH TIGHT; NARROW TXWYS. HE SAID HE APPRECIATED THE CALL; AND NO ACTION WOULD BE TAKEN. THE SIGNAGE ON THE ARPT FOR DOUBLE ALPHA WAS OFF TO THE R; ADJACENT TO TXWY P AND NOT NEAR RWY 13. NEXT TIME I'LL DELAY THE PA TO THE PAX UNTIL CLR OF ALL RWYS. SUPPLEMENTAL INFO FROM ACN 620894: I MADE A QUICK PA TO LET THE PAX KNOW WE HAD TO RETURN TO THE GATE AND TO STAY IN THEIR SEATS. WHEN I RETURNED FROM THE PA; THE CAPT WAS RESPONDING TO TWR TO HURRY ACROSS RWY 22 AND TURN R ON TXWY L. THE SIGNAGE FOR DOUBLE ALPHA IS HARD TO SEE AND FARTHER FROM THE RWY THAN OTHER TXWY SIGNS. THIS LED TO THE MISSING OF THE TXWY; AND SUBSEQUENT XING OF RWY 22.