ZDC CTLR EXPERIENCED OPERROR AT FL340 WHEN A FAILED HDOF ATTEMPT RESULTED IN AN ACFT OVERTAKE.

Narrative

I TOOK HDOF ON A WILMINGTON; DE; ARR (ILG) AT FL410. I NORMALLY HAVE THE ARPT DISPLAYED IN THE 4TH LINE OF THE DATA BLOCK; BUT A SPD WAS DISPLAYED INSTEAD FOR THIS PARTICULAR ACFT. THE SECTOR 2 BELOW MINE IS REQUIRED TO HAND OFF TO THE NEXT CTLR ILG ARRIVALS AT FL230. WHEN THE CTLR I WAS ATTEMPTING TO HAND OFF THE LJ60 TO NOTIFIED ME HE COULD NOT ACCEPT THAT ACFT; HE WAS 10 MI FROM THE BOUNDARY; FORCING ME TO VECTOR THAT ACFT WBOUND INTO HVY TFC FOR HIS DSCNT. THE SECTOR BELOW MINE WAS SLOW IN TAKING THE HDOF OF THE LJ60; AND DUE TO THAT ACFT'S SPD; HE CAUGHT UP WITH THE B737 BEFORE THE CONFLICT ALERT ACTIVATED. ALSO; THE FREQ IS VERY BAD AT THAT SECTOR; AND THE LJ60 DID NOT DSND WHEN I FIRST ISSUED THE CLRNC. THERE WOULD HAVE BEEN NO PROB WITH THIS ACFT IF ILG ARRS ON J42 WERE RESTR TO CROSS 15 MI W OF MONTEBELLO AT OR BELOW FL290. THE PREVIOUS SECTOR IS REQUIRED TO DSND PHL ARRS TO FL330 AT THAT POINT; AND THEY ARE ALLOWED TO CROSS THE SAME POINT ILG ARRS HAVE TO BE AT FL230 AT FL290. HOWEVER; THERE IS NO SOP FOR ILG ARRS BTWN MY SECTOR AND THE PREVIOUS SECTOR. UNTIL THERE IS; THE SITUATION THAT HAPPENED TO ME COULD HAPPEN TO OTHERS VERY EASILY.