ACR DEP FROM MCO IS DENIED WX DEV FROM ZJX AND ENCOUNTERS TSTMS AND TURB.

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WHILE CLBING OUT ON THE MCOY 9 DEP FROM MCO; WE SAW A NARROW BAND OF TSTMS OVER THE GUANO INTXN. WE QUERIED ATC (JACKSONVILLE) ABOUT A POSSIBLE L (310 DEG HDG) OR R (010 DEG HDG) DEV TO AVOID THE WX. ATC REPLIED WITH A HIGHER ALT SUGGESTING WE CLB OVER IT INSTEAD. AS WE CONTINUED TO CLB; WE REALIZED WE WOULD NOT GET OVER THE TOP OF THE STORMS AND ASKED ATC FOR A WBOUND HDG (300 DEGS OR SO) TO AVOID THE WX AHEAD. ATC DENIED OUR REQUEST AND ASSIGNED A NORTHERLY HDG (010 DEGS) INSTEAD; BUT THE STORMS WERE ALREADY CLOSING IN AND WE DIDN'T HAVE SUFFICIENT TIME TO AVOID. USING OUR WX RADAR; WE TRIED TO DEV BTWN THE WORST PARTS OF THE WX AS WE PENETRATED. WE MANAGED TO AVOID THE STRONGER CELLS BUT STILL PENETRATED THE WEAKER ONES WHICH GAVE US HVY LIGHT TO MODERATE TURB. DURING THE ENTIRE ORDEAL; WE HAD THE ACFT TRIMMED FOR MAX PERFORMANCE CLB; WHICH WAS DECREASING OUR SPD AS WE CLBED. I SHALLOWED THE CLB RATE TO MAINTAIN OUR SPD ABOVE 210 KTS. AS WE ENTERED THE WORST TURB; I DISCONNECTED THE AUTOPLT AND THE PLI BEGAN TO POP IN AND OUT OF THE PFD SCREEN. WE WERE GETTING VARIATIONS IN AIRSPD BTWN 190 KTS AND 205 KTS. THE TURB WAS NEVER WORSE THAN MODERATE BUT THE DRAFTS WERE CAUSING THE ACFT TO PITCH UP AND DOWN TO THE POINT WHERE THE STICK SHAKER WAS ACTUATED AND THE AIRSPD VARIED. I APPLIED MAX THRUST (TO RSV) TO MAINTAIN A POSITIVE RATE OF CLB WHILE MAINTAINING AIRSPD; AND WE EXITED THE TOP OF THE CLOUDS WITHIN 10-15 SECONDS AND ALL OF THE WX WITHIN 30 SECONDS. SOON AFTER; WE LEVELED AT OUR CRUISING ALT OF FL310 AND WE HEARD OTHER ACFT REQUESTING THE SAME DEVS WE REQUESTED. ATC ONCE AGAIN DENIED THE REQUESTS AND SUGGESTED THAT THEY ALSO CLB TO A HIGHER ALT AND GET ON TOP OF THE WX. THE OTHER ACFT ADVISED ATC THEY WOULD BE UNABLE TO CLB ABOVE IT AND NEEDED TO TURN INSTEAD. ATC WAS SILENT FOR A MOMENT AND I ADVISED THEM NOT TO ATTEMPT TO CLB THE WX BECAUSE IT WAS BUILDING FASTER THAN OUR ACFT COULD CLB. ACR Y PROCEEDED TO ASK ATC FOR A TURN; BUT NO RESPONSE WAS GIVEN. EVENTUALLY; ATC TOLD THE OTHER ACFT TO DEVIATE AS NECESSARY AND THE CORRIDOR WAS SHUT DOWN TO ALL NBOUND AND SBOUND ACFT. HAD WE GOTTEN OUR ORIGINAL REQUEST TO DEVIATE FROM THE WX; ALL OF THIS SIT WOULD HAVE BEEN AVOIDED. ATC TRIED TO HELP US BY TELLING US TO CLB BECAUSE OTHER ACFT WITH MUCH BETTER PERFORMANCE OUTCLBED THE WX AND DIDN'T RPT ANY PROBS. I TAKE RESPONSIBILITY FOR NOT 'STICKING TO MY GUNS' AND CONTINUED MY REQUEST FOR A DEV OR A 180 DEG TURN INSTEAD OF A CLB; BUT THE CTLR SHOULD HAVE REALIZED OUR NEEDS SINCE WE KEPT TELLING HIM THAT THE WX WAS WORSE THAN DEPICTED ON OUR RADARS AND WE NEEDED ANOTHER SOLUTION THAN SUGGESTED.