PLT OF GOV OPERATED BE30 IS VECTORED INTO SUA BY PCT WHILE DEPARTING THE DC ADIZ AREA IN VMC.

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WE HAD JUST COMPLETED OPS AT DAVISON AAF AND WERE REPOSITIONING VFR TO RICHMOND; VA; APPROX 65 NM TO THE S. WE CONTACTED POTOMAC APCH SLIGHTLY W OF DAVISON AAF AND INFORMED THE CTLR WE WISHED TO PROCEED VFR AT 6500 FT AND WOULD LIKE ADVISORIES TO RICHMOND. WE WERE INSTRUCTED TO FLY HDG 180 DEGS AND MAINTAIN 2500 FT; AS THAT WAS THE CLASS B FLOOR IN OUR AREA. MOMENTS LATER; WE WERE CLRED TO 3500 FT AND GIVEN A FREQ CHANGE TO A DIFFERENT SECTOR. WE HAD DIFFICULTY MAKING AN INITIAL CALL TO APCH DUE TO A VERY INVOLVED RADIO CONVERSATION TAKING PLACE BTWN ATC AND A COMMUTER ACFT. I WOULD ESTIMATE IT TOOK 5-6 ATTEMPTS TO REACH ATC; BUT EVENTUALLY WE WERE SUCCESSFUL. WE TOLD THE CTLR OUR HDG AND ALT AND WE WERE GOING TO RICHMOND AND THAT WE WANTED HIGHER. WE WERE TOLD TO MAINTAIN 3500 FT AND VFR. A FEW MINS LATER; WE WERE TOLD TO CONTACT ANOTHER POTOMAC SECTOR; NEVER GETTING APPROVAL TO CLB. WHEN I CHKED IN WITH THE FINAL CTLR; I TOLD HIM THAT WE WERE VFR AT 3500 FT LNDG AT RICHMOND. A FEW MOMENTS LATER; HE ASKED US TO CLB TO 5500 FT AS WE HAD ENTERED RESTR AIRSPACE. WE MADE THE CLB AND CONTINUED THE FLT TO RICHMOND. MY OVERALL IMPRESSION OF THE EVENTS ARE THESE: I COULD HAVE PAID MORE ATTN TO OUR GND TRACK ON THE SECTIONAL AND QUESTIONED ATC MORE FORCEFULLY AS TO THE AIRSPACE CONFLICT. I ALSO BELIEVE THAT ATC MIGHT HAVE HELPED PREVENT THE SIT BY WARNING ME OF MY PROX TO RESTR AIRSPACE OR AT LEAST GRANTING MY REQUEST TO CLB AS REQUESTED. I BELIEVE THE SECOND CTLR WAS SATURATED AT THE TIME WE TRIED TO COMMUNICATE WITH HIM; AND THAT SATURATION RESULTED IN A VERY LATE HDOF WITH NO CHANGE OR A WARNING CALL TO AVOID RESTR AIRSPACE FROM THE FINAL CTLR.