B737 AT FL240 DEVIATES AROUND WX AND ZAB DECLARES EMER.

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ENRTE TO MOHAK ON ARLIN ARR AT FL270; I TOLD CAPT TO REQUEST 5-10 DEGS R FOR TSTM OVER MOHAK; CURRENTLY 60+ MI AWAY AND PAINTING WELL. CAPT ASKED ZLA; WHO INSTEAD DELAYED US AND HAD US DSND TO CROSS MOHAK AT FL250. I DSNDED TO FL250 SOON AFTER AND AS WE GOT CLOSER TO MOHAK AND THE STORM; ZLA HANDED US OFF TO ZAB. JUST PRIOR TO THIS; WE STARTED DEVIATING TO THE S ABOUT 10 DEGS; OR 080 DEG HDG IF MEMORY SERVES ME. I TOLD THE FLT ATTENDANTS TO STAY SEATED AND MADE A PA TO THE PAX REGARDING THE WX AND THE NEED TO GO AROUND IT. ZAB WAS IMMEDIATELY CONCERNED WITH OUR SOUTHERN DEV/HDG AND ASKED US TO ACCEPT A 055 DEG HDG IF POSSIBLE; WHICH WOULD HAVE TAKEN US THROUGH THE STORM CENTER. WE SAID NO; BUT TOLD THEM WE WOULD ONLY NEED THE DEV TO 080 DEGS FOR 10 MI OR SO. WE BEGAN CORRECTING BACK TO TRACK ON THE ARLIN WHEN ATC TOLD US TO SQUAWK 7700; LEADING US TO THIS RPT. BY THAT TIME WE WERE ALREADY BEGINNING TO CORRECT BACK TO TRACK QUITE QUICKLY; BUT WE DID AS WE WERE TOLD WITH THE SQUAWK. WE MENTIONED THAT WE ASKED ZLA A LONG TIME BACK ABOUT THE WX (TOPS FL290 FROM OUR GUESS AND A PIREP HEARD EARLIER WITH ZLA). ABQ MENTIONED THAT ZLA HAD BEEN TOLD TO ALLOW NO DEVS TO THE S AND WERE NOT COMPLYING TOO WELL. WE WERE SOON GIVEN MAX FORWARD SPD AND DIRECT PAYNT ON THE ARR; AND REGAINED OUR PREVIOUS SQUAWK A FEW MINS LATER ON OUR REQUEST. THE PROX OF THE STORM TO THE 2 CTR'S BOUNDARIES MADE THIS A COORD PROB FOR THEM OBVIOUSLY. WE GAVE ZLA PLENTY OF TIME TO COORDINATE; BUT ALL THEY DID WAS GIVE US A DSCNT; WHICH DIDN'T HELP AT ALL. WE MAINTAINED AS CLOSE TO ON TRACK AS SAFETY ALLOWED; AND HAD ATC DISAPPROVED A REQUESTED DEV; WE WOULD HAVE HAD TO DECLARE AN EMER ON OUR OWN; BUT THEY TOOK CARE OF THAT FOR US. SAFETY REQUIRED A DEV; ATC DELAYS IN COORD REQUIRED IT TO BE SOUTHERLY BY THE TIME WE HAD TO ACT. UNFORTUNATELY; THAT WAS NOT THE PREFERRED DIRECTION; BUT I DON'T FLY THROUGH TSTMS FOR ANYONE.