B737 DEPARTING MCO OPPOSITE DIRECTION TO OTHER TFC EXPERIENCED TCASII RA WITH ARR ACFT.

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WE HAD A TCASII RA THIS MORNING ON DEP. ACTIVE RWY WAS RWY 35 (RWY 36L/4). PUSHED OFF GATE AND LISTENED CAREFULLY TO SEE HOW BUSY TAXI OPS WERE. ALL SEEMED QUIET; ONLY 1 ACFT TAXIING FOR RWY 35; SO WE ASKED FOR OPPOSITE DIRECTION DEP OFF RWY 17 TO HELP SAVE TIME WITH WINDS WITHIN LIMITS. GND CTL PUT CONSIDERABLE TIME INTO COORDINATING. TWR APPROVED AND CLRED US FOR TKOF IMMEDIATELY. DEP WAS EXPEDITIOUS AND SMOOTH ON AN ASSIGNED HDG OF 220 DEGS AND CLB TO 5000 FT. SWITCHING OVER TO DEP; IT BECAME APPARENT THAT THINGS WERE MUCH BUSIER THAN ON GND CTL. WE WERE ASSIGNED A NEW HDG OF 300 DEGS (R TURN TO N) AND CLB TO 1400 FT. TFC FOR US WAS FLT NUMBER HVY AT 2 O'CLOCK POS; DSNDING THROUGH 7700 FT ON A SOUTHERLY HDG. BOTH ACFT WERE VISUAL ON EACH OTHER. WE WERE R WING DOWN IN THE TURN FOR 300 DEGS; SO I COULD NOT IMMEDIATELY SEE FLT NUMBER; BUT MY FO HAD HIM THE ENTIRE TIME AND STATED THAT HE WAS NOT COMFORTABLE WITH THE GEOMETRY. MONITORING ON THE VSI TCASII DISPLAY; I COULD SEE ACR Y APCHING 2 MI AND DSNDING/CLOSING 900 FT ABOVE US. I MOMENTARILY ROLLED WINGS LEVEL FROM THE TURN AND SHALLOWED THE CLB IN AN ATTEMPT TO DECONFLICT AND HONOR THE FO'S CONCERNS. THIS WAS QUICKLY FOLLOWED BY A CLB RA OF ABOUT 200 FPM THAT LASTED A COUPLE OF SECOND AND THEN TCASII CHANGED ITS MIND AND ISSUED AN IMMEDIATE DSND RA OF ABOUT 1400 FPM. WE HONORED THIS ONE; STOPPED CLBING AT 5600 FT AND DSNDED BACK DOWN TO APPROX 600 FT. ACR Y CLRED ACFT AND ABOVE AT ABOUT 1 - 1 1/2 MI. WE TRIED TO TELL ATC ABOUT THE RA; AND MOMENTARILY DSCNT; BUT THE FREQ WAS VERY CONGESTED. ONCE WE HEARD 'CLR OF CONFLICT' WE VERIFIED OUR CLRNC TO 14000 FT AND CONTINUED R TO 300 DEG HDG. REST OF CLBOUT UNEVENTFUL. LESSONS LEARNED: I FELT SOME PRESSURE TO TRY AND MAKE UP TIME WITH AN OPPOSITE DIRECTION TKOF WHICH RESULTED IN AN INCREMENTAL INCREASE IN THE 'EFFICIENT 'ON TIME' PRINCIPLE.