How long is the M25? By my calculation its 118½ miles per lap which includes 5 miles or so of the A282 that connects junction 31 to junction 2 via the QEII Bridge, Dartford Tunnels and junctions 1A and 1B. Your mileage may vary (+/- 175 yards) depending on direction of travel. The idea of saving time by cutting corners on the M25 is a non starter since there are no short cuts and it takes around an hour to complete half a lap vs an 1¾ hours to cut across London.
So 9 laps would make a challenging 1,066 miles, expect high volumes of traffic, variable speed limits and reassuringly expensive fuel prices. Start and finish at a Service Station of you choice, there are four South Mymms and Thurrock are both off the M25 making Clacket Lane or Cobham a better choice. Grab a receipt and odo photo on each lap as a lap counter and I don't see where there would be a verification problem, best to get it pre-verified to be sure, to be sure.
Of interest there have been two 'M25 clubs' that I know of, pretty sure neither exists today. The first was a 'Top Gear' type club where membership was achieved by lapping the M25 in under an hour, of the many claims few where verified and none made entry into the Guinness Book of Records. The other M25 club was a 'M25 lap club', membership was achieved and certificates issued by lapping the M25 in both directions at your leisure but in one continuous drive/ride save for fuel and comfort breaks. There were reports of folk taking over 12 hours or more to complete both laps.