MD80 FLC REQUESTS EITHER HIGHER ALT OR A DEV AROUND WX AHEAD NEAR PIE; FL. CTR CTLR CANNOT ACCOMMODATE REQUEST. PIC DECLARES EMER AND DEVIATES. PIC COMPLAINT OF COM PROB WITH CTR ACCOUNT TFC.

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ON CLB OUT FROM SRQ WE LEVELED OFF AT FL210 AT ATC REQUEST AND DEVIATED TO THE E AROUND WX (TSTM) THAT WAS IN THE PIE-TPA AREA. ATC ASSIGNED US A 350 DEG HDG. AS WE PROCEEDED N WE SAW THAT WE MUST EITHER CLB OR DIVERT TO THE E TO AVOID THE TSTMS. WE REQUESTED HIGHER AND DID NOT RECEIVE ANY RESPONSE DUE TO THE CTLR BEING VERY BUSY. WE REQUESTED HIGHER AFTER 2 OR 3 MINS AND WERE TOLD IT WAS NOT AVAILABLE. AT THAT TIME WE REQUESTED A R TURN TO 030 DEGS. WE WERE TOLD THAT WAS UNAVAILABLE. AT THIS TIME WE TOLD ATC THAT WE MUST TURN TO AVOID THE TSTM AND ATC ADVISED THAT WE WOULD HAVE TO USE OUR EMER AUTH IF WE WANTED TO TURN. WE SQUAWKED 7700 AND MADE A TURN TO 030 DEGS WHICH WE ADVISED ATC OF. WHEN WE WERE ABLE TO FLY 350 DEGS AGAIN WE ADVISED ATC THAT WE WERE ABLE TO AND TURNED TO 350 DEGS. ATC ASSIGNED US A NEW SQUAWK AND CLBED US TO FL260 AT THIS TIME. WE CLBED TO FL260 AND CONTINUED OUR TRIP. ADDITIONAL INFO: ATC WAS VERY BUSY AND UNABLE TO RESPOND TO SEVERAL REQUESTS FROM BOTH US AND OTHER ACFT.