PLT OF ATX OVERSHOT ASSIGNED ALT DEPARTING LAKE FRONT ARPT BECAME CONFLICT FOR MLG APCHING CLE.

Narrative

THE CLRNC FROM THE BURKE LAKEFRONT GND CTLR WAS THE SAME ONE THAT I GET EVERY NIGHT; (CLRED AS FILED TO THE SMITH FIELD ARPT; CLB AND MAINTAIN 2000 EXPECT 4000 WITHIN 10 MINS). THE L ENG RPM'S DID NOT RESPOND TO THE L PROP CTL. I BELIEVE THAT ABOUT THIS TIME I WAS HANDED OFF TO THE CLEVELAND DEP CTLR. HDOF INSTRUCTION WAS ABBREVIATED; 'CONTACT DEP ON 124.0.' WHEN I RECEIVED THIS HDOF; I NOTICED THAT MY ALT WAS APPROX 2700 AND CLBING RAPIDLY. I REMEMBER THINKING THAT I WAS CLRED BY THE BURKE LAKEFRONT TWR TO 4000. SINCE I THOUGHT THAT I WAS CLRED ON UP TO 4000; I MADE NO ATTEMPT TO CORRECT THE CLB RATE; AND CHKED ON WITH CLEVELAND APCH BY STATING; 'CLEVELAND APCH SMT X IS WITH YOU OUT OF 2.8 FOR 4000.' THE CTLR IMMEDIATELY RESPONDED THAT I SHOULD BE AT 2000; AND THAT THIS ALT WAS DUE TO A POTENTIAL CONFLICT WITH AN MLG THAT WAS ON AN ILS APCH TO THE CLEVELAND HOPKINS ARPT. I PUT MY ACFT INTO AN IMMEDIATE STEEP DSCNT THAT MAY HAVE EXCEEDED 2000 FPM. UPON REACHING AN ALT OF 2400; I WAS CONTACTED BY THE CTLR AND ADVISED THAT TFC WAS NO LONGER A FACTOR AND I COULD NOT CLB TO 4000. I WAS HANDED OFF TO TOLEDO APCH CTLR; AND ADVISED TO CONTACT THE CLEVELAND ATC FACILITY AT TELEPHONE. I SHOULD ALSO MENTION THAT AT THE TIME OF THE CONFLICT; AND NEAR MISS; I OVERHEARD A CONVERSATION BTWN THE MLG AND THE CLEVELAND ATC. THE MLG PLT ASKED THE CTLR WHAT MY ALT WAS AND THE CTLR RESPONDED THAT MY ACFT WAS AT 2800. THE PLT RESPONDED; I'M SURE GLAD THAT I DIDN'T DO WHAT MY TCASII EQUIP TOLD ME TO DO. IT TOLD ME TO DIVE. THE ATC CTLR AGREED.