Interesting question
Assuming that the exact terms and conditions of the record are along the lines of single seat, single piston engine land plane, I think that a P51D would be the ideal candidate to have a go at the record due to its combination of range and speed.
Having said that, I wonder how easy it would be nowadays to get all the clearances necessary to fly through all the various jurisdictions in a veteran warbird!
Of course that isn't much younger than the Mew Gull! So reliability might be a big problem.
I too would be interested to hear what other people's suggestions would be for a modern aircraft to attempt the record. I can't think of anything that would combine the requisite speed and range, even with mods to increase fuel capacity.
Post-war, fast single seat aircraft seem to be geared more towards aerobatics and have limited range, whereas 2 or 4 seat tourers might have more provision for fuel but haven't got the speed.
And what other restrictions would the modern would-be record breaker face?
SD