Most people would use the Normal Takeoff procedure
Providing the length substantially exceeds the standard data, and the terrain profiles are benign, the normal takeoff can be converted into the standard speeds should a need arise.
How much more? A lot more
To a rough first approximation the distance ratio will go up as the speed ratio squared eg speed up 20%, then distance up probably in excess of 45%
it is because we use long runways
Indeed .. which is why the problems arise when folks, used to long runways, find themselves playing out in the woods with seriously short strip lengths. The croppies and tug pilots, having had some training and exposure to these concerns, generally show a high degree of conservatism .. if they are to survive to retirement age.
my approach would be to use a higher altitude/lower temperature giving the same density altitude and enter the chart that way.
On what basis ? Not being wary of extrapolating to higher elevations and OATs might present problems. Things aren't necessarily linear.
For the typical non-engineering pilot, I would suggest don't extrapolate high. If the elevation/temperature is lower than the the chart data, and there are no other systems limitations prescribed in the limitations section, maybe .. and, in that case, use the published data without trying to take advantage of extrapolation.
I would be interested in djpil and JT comments.
I think Dave and I would opine along the lines that we would, first, like to know a bit about the aircraft's engines, airframe configuration, etc ... ie better not to wing it on the fly as it were .. Mr Walker's (and I have no idea who he is) comments are the go .. as I suggested earlier, if the operator has a problem with the POH, do some accredited testing and reschedule the performance data .. get a tick in the box .. and Robert's your parent's sibling.