FLC OF AN LGT OVERSHOT DSCNT ALT AND XING FIX SPD RESTR.

Narrative

WE WERE ON VECTORS TO AVOID TSTMS DSNDING INTO MIAMI. WHEN ABLE TO AVOID TSTMS; WE WERE CLRED DIRECT TO WORPP (CLE 110 DEGS 46 NM). CTR SAID WE WERE #1 AND KEEP THE AIRSPD UP. WE WERE NOW CLRED TO CROSS WORPP AT 250 KIAS AND 10000 FT. THE FO WAS FLYING AT 315 KIAS. AS WE DSNDED THROUGH 14000 FT; CTR CALLED AND WHAT WE THOUGHT WAS; MAINTAIN 13000 FT FOR TFC; THAT IS WHAT WE READ BACK. THERE WAS OTHER COM TFC THAT OVERRODE OUR INCOMING AND OUTGOING XMISSIONS. CTR SOON CALLED AND ASKED; WERE WE GOING TO MAKE WORPP AT 10000 FT? THAT'S WHEN WE DISCOVERED THE MISCOM. I HAD ASKED THE FO TO SLOW THE ACFT DOWN BECAUSE OF CUMULUS BUILDUPS UP TO 11000 FT. HE ARGUED WITH ME BECAUSE CTR ASKED US TO KEEP THE AIRSPD UP. I WAS ABOUT TO TELL CTR ABOUT OUR DECREASED AIRSPD. NOW WHEN CTR ASKED ABOUT US GETTING DOWN TO 10000 FT; THE CLOUDS WERE BEHIND US. THE FO WAS SLOWING DOWN TO GET THE 250 KIAS SPD UNDER CTL. I TOLD HIM TO GET DOWN TO 10000 FT FIRST WITH SPD BRAKES OUT AND THEN GET THE 250 KIAS BECAUSE ALT WAS MORE CRITICAL. HE STARTED ARGUING WITH ME AGAIN WHILE IN DSCNT AND RAN THROUGH 10000 FT DOWN TO 9400 FT AND THEN CAME BACK UP TO 10000 FT. THERE WAS HEATED DISCUSSION IN THE COCKPIT DURING AN ATTEMPTED CRITIQUE. I BELIEVE; WX; COM; CHANGING CONDITIONS AND PRIORITIES WERE ALL TESTED.