C414 PLT ENTERED CLASS C WITHOUT CLRNC.

Narrative

WE WERE TRANSPORTING A CRITICALLY ILL PATIENT FROM ZZZ TO ZZZ1; UNDER A VFR FLT PLAN. USING A SPECIFIED CALL SIGN. WE OPERATED THE ENTIRE FLT AT 2000 FT MSL; BELOW WHICH IS NOT UNUSUAL FOR SUCH A SHORT FLT. WHEN OPERATING ON THIS RTE IN THE PAST; I HAVE ALWAYS CONTACTED ZZZ APCH PRIOR TO APCHING THE 20 NM OUTER RADIUS OF ZZZ CLASS C AIRSPACE. AS I APCHED 20 NM FROM ZZZ; THERE WERE NUMEROUS UNCTLED VFR TARGETS OPERATING IN THE VICINITY -- SOME LEGALLY INSIDE; BUT BELOW THE 2000 FT FLOOR OF THE 20 NM OUTER SHELF OF CLASS C AIRSPACE. AS ALWAYS; WE WERE USING THE COMMON TA FREQ (CTAF) TO SEPARATE OUR ACFT FROM THE UNCTLED TFC IN THE AREA. BECAUSE I WAS ALSO ALREADY BELOW 2000 FT; AND ZZZ APCH WOULD NOT BE ABLE TO PROVIDE SEPARATION FROM THE UNCTLED TFC INSIDE AND BELOW THE 20 NM SHELF; I WAS OBLIGATED TO ACTIVELY USE THE CTAF IN ORDER TO SAFELY PROCEED. IN LIGHT OF OUR URGENT LIFEGUARD MISSION; WE ESTABLISHED 2-WAY RADIO COM WITH ZZZ APCH PRIOR TO ENTERING THE 5 NM INNER RADIUS OF CLASS C AIRSPACE. AFTER ASSIGNING A XPONDER CODE; ZZZ APCH MOMENTARILY PAUSED AS WE ACKNOWLEDGED AND CONTINUED INBOUND. AFTER ASKING US TO RESTATE OUR POS; ZZZ APCH IMMEDIATELY HANDED US OFF TO ZZZ TWR. ZZZ TWR MAY NOT HAVE GOTTEN THE HDOF; BECAUSE THEY WERE CONFUSED AS TO OUR POS AND INTENTIONS ON R DOWNWIND. I THEN REALIZED THAT TFC SATURATION AT THE FIELD WAS TOO HIGH; AND MADE A L TURN TO THE E IN AN ATTEMPT TO DEPART THE TFC. I WAS THEN INSTRUCTED TO MAKE A R 360 DEG AND HOLD OUR POS. BEFORE BEING ABLE TO MAKE THE TURN; WE WERE GIVEN CLRNC TO LAND 'SHORT APCH.' I FEEL THE SIT MAY HAVE BEEN PREVENTED IF: ZZZ APCH INSTRUCTED US TO 'REMAIN CLR OF CLASS C IF TFC SATURATION WAS TOO HIGH.' THE NE 20 NM RADIUS FLOOR IS EXTENDED TO THE SURFACE.