A B727 FREIGHTER FLC RPT ON RUSHING AN INST APCH INTO COS AND EXPERIENCING AN ALTDEV ALT OVERSHOT AND A STICK SHAKER. A POSSIBLE OR NEAR CFIT.

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ORIGINALLY WE WERE SCHEDULED MEM-COS-GJT. COS WX BELOW MINIMUMS AND FORECAST TO REMAIN THAT WAY. FLT WAS DISPATCHED FROM MEM DIRECTLY TO GJT. I DID NOT NOTICE THE 'NON TWR OPS N/A' MESSAGE ON THE FLT PLAN RELEASE. DUE TO COS OVERFLT; WE WERE SCHEDULED TO ARRIVE AT GJT 20 MINS PRIOR TO ATCT OPENING. WE BECAME AWARE OF THIS FACT WHEN COMPANY SELCALLED US ABOUT 15 MINS AFTER DEP. COMPANY SAID TO 'FLY SLOW OR TAKE THE SCENIC RTE' UNTIL THEY COULD GET AUTH FROM THE DUTY OFFICER FOR A NON-TWR LNDG. WE WERE TOLD TO EXPECT A SELCAL AROUND COS GIVING US AUTH TO LAND AT GJT BEFORE THE TWR OPENED. SELCAL CAME AROUND 20 MI S OF COS. CAPT WAS SURPRISED WHEN THE FLT CTLR SAID THE WX AT COS WAS NOW ABOVE MINIMUMS AND COULD WE GO THERE NOW? SURPRISED BECAUSE HE HAD JUST LISTENED TO ATIS ABOUT 5 MINS EARLIER AND IT SAID WX WAS STILL 1/4 MI. WE TALKED DIRECTLY TO COS TWR AND WX WAS INDEED ABOVE MINIMUMS; SO WE ASKED CTR FOR A RERTE (WE WERE ONLY ABOUT 15 MI AWAY AT THIS TIME; FL280). CLRED TO BLACK FOREST VOR AND DSND TO 9000 FT. WE WERE ALL EXTREMELY BUSY. FO WAS FLYING; SO WAS COPYING DIVERT INFO AND ARR WX AND CALCULATING LNDG PERFORMANCE. CAPT WAS GETTING OUT COS PLATES/BRIEFING APCH (ILS RWY 174). DECIDED TO CONDUCT A MONITORED APCH AS WX WAS JUST ABOVE CAT I MINIMUMS. FO WAS DSNDING FAST WITH SPD BRAKES OUT. AS WE APCHED 9000 FT MSL; APCH GAVE US AN INTERCEPT VECTOR FOR THE ILS AND SAID TO MAINTAIN 9000 FT UNTIL ESTABLISHED. FO THOUGHT HE HEARD 8000 FT AND QUERIED ME. CAPT WAS TALKING TO APCH AND DID NOT HEAR HIM. CAPT 'WEARS' THE SENNHEISER HEADSET AND IT IS VERY QUIET BUT ALSO SOMETIMES HARD TO HEAR COCKPIT CONVERSATION AND AURAL ALERTS; FO CONTINUED DSCNT BELOW 9000 FT. CAPT DID NOT HEAR THE AURAL ALERT AS WE WENT BELOW 8700 FT. CAPT WAS TUNING THE ILS AS ACFT WAS IN A L-HAND TURN TO THE INTERCEPT HDG (140 DEGS?). AT 8500 FT APCH CAME ON AND SAID 'DON'T DSND BELOW 9000 FT UNTIL ON THE LOC.' FO IMMEDIATELY APPLIED GAR PWR AND RAISED THE NOSE RAPIDLY. SPD BRAKES WERE STILL EXTENDED AND STICK SHAKER ACTIVATED. (SPD WAS 10 KTS ABOVE 0 DEG BANK MINIMUM MANEUVERING SPD.) CAPT ASKED FO TO ROLL WINGS LEVEL WHICH HE DID. SPD HAD DECAYED BELOW 0 DEGS MINIMUM MANEUVERING SPD SO CAPT SAID HE WAS GOING TO FLAPS 2 DEGS. INFLT WARNING HORN SOUNDED DUE TO SPD BRAKE EXTEND/FLAPS EXTEND. HE IMMEDIATELY RETRACTED SPD BRAKES AND WE IMMEDIATELY CLBED BACK TO 9000 FT. AT THIS POINT HE ASKED APCH TO VECTOR US BACK AROUND TO INITIATE ANOTHER APCH. THIS WE DID AND COMPLETED THE APCH AND LNDG WITHOUT FURTHER INCIDENT. WE DON'T BELIEVE THAT WE GOT BELOW 8500 FT AT ANY TIME BEFORE GS INTERCEPT. FACTORS WERE CREW FATIGUE; PERCEIVED NEED TO HURRY DUE TO CLOSE PROX TO COS AT TIME OF RERTE. DISCUSSED WHAT HAPPENED WITH CREW AFTER LNDG AND ALL AGREED THAT WE SHOULD HAVE LOITERED TO THE E OF COS UNTIL WE WERE ALL UP TO SPD AND READY TO COMMENCE THE APCH. SUPPLEMENTAL INFO FROM ACN 419984: WE WERE GIVEN A DSCNT TO 9000 FT FROM CTR AND HANDED OFF TO APCH. WHEN CHKING IN WITH APCH THEY SAID MAINTAIN 9000 FT AND I THOUGHT THEY SAID 8000 FT CLRED FOR APCH. WE SHOULD NOT HAVE STARTED THE APCH YET; WE WERE RUSHING.