A B757 Captain reported an unstabilized approach following a high speed arrival to the airport because of medical emergency on board.

Narrative

Cruising at FL370 when a medical emergency arose. Requested priority handling with Center. Direct routing provided and paramedics and ambulance arranged. After descending for approach and on final; ATC cleared us for approach. Had kept speed up to expedite arrival. Began to slow and at FAF had gear down and flaps to about 15 degrees. Reported 20 KT tailwind inside FAF but airport was reporting calm to 5 KTS out of the south. Called for flaps 20 degrees and they were put out. IAS is now approximately 180-185 KIAS. Called for Flaps 25 degrees; at or below flap speed for that setting. At this point the IAS was above 165 KTS which would not allow the final flaps to be selected. Pulled power back; displaced spoilers slightly; but was not configured for final approach at 1000 FT as is SOP. Speed finally bled off to below 162 KTS; lowered spoilers; requested Flaps 30 degrees at about 700 FT AGL. Flaps reached landing configuration at about 300-400 FT AGL. Normal landing was accomplished. Did not notice a low speed warning nor a GS warning during the approach; but we were not in the landing configuration or slot at the appropriate altitude on final. Go Around should have been considered. Several contributing factors: Trying to rush to landing destination due to medical emergency. Not allowing for enough time or distance to slow aircraft (winglets installed) to proper FAF speed; approximately 160 KTS with the flaps at 20 degrees. Also not compensating for the 20 KT tailwind at 2;000-3;000 FT. And because the whole approach was executed in VFR conditions and with a long runway in front of me I did not consider the landing to be unattainable in a safe and considerate manner. At 300 FT over the end of the runway; I had probably let go around slip from my list of alternatives.