Had to happen sooner or later in 2012!
Ok, I have read what you asked BigMart and I think (wow that hurts) this:
250 miles. When we rode to Stonehenge and beyond, I clocked 250 miles counting from out of the door etc until the battery ran out and determining the rest via ridewithgps blah blah (want to give me a pipe yet?) We tooled around quite a lot and, with mechanicals, arrived back to the Cenotaph 24 hours after leaving. The return bit along the A4 was 'paced' as I asked Davy to keep it at 18mph so we all stayed together. Lot to be said for riding and sharing.
When you, Ian, Rimas and I did the return from Harwich, I covered 202 miles - your distance was similar. The return leg was tight, and rapid until we went our separate ways and, starting at midnight, I arrived back about 6:30pm? Probably we only dropped three hours on that ride?
Riding London to Cardiff was 145 miles I think. Lots of casual stops and mechanicals etc - Frank and I arrived at 11:30pm - that would be about 12 hours riding?
Also, young Andy and Rob kicked off from Sheffield early one morning and we were rolling down the A5 about 7pm - Adam will have better details than I, but it was a good day's riding for them. Young fit boys but with Adam and I holding them back, of course...Sheff to Nelson is about another 50 miles+ roughly?
All that to say - I would advise starting at midnight and making a decision about continuing or stopping a lot earlier in the day. It is a long haul on your own, although do-able of course. Also that is a 15+mph average for the duration - some will be quicker, some slower. Even philistines need to stop. Maybe not for you Morris Dancing or scenic views of Ancient Monuments (save for the odd group photo of Simon, Adrian, User10571, Greg etc) but even you will run out of things to talk to yourself about, and you'll need 'input'. And 'output'.
Could be that a kind soul or two (young fit students based in Sheffield perhaps?) might like to ride up with you...Three extras gets a groupsave! Better still, make it a 'H4H ride' and Luke might come out of the woodwork!

I didn't vote either...