Trying to lump things into a simplistic "so many seconds to a specific speed" probably is not a great deal of value for the wide range of jet performance seen these days.
The military places some reliance on runway distance boards for the concerns suggested in the OP's post. However, unless you have some objective data it gets a bit hard to come up with homegrown techniques which hold much water.
Having said that, I see no problem, in the usual absence of such data in civil manuals, with a pilot's developing some data for his/her Type by measured observations on the line. One is not trying to obtain anything like precise data, rather gross, indicative data which should alert the thinking pilot to significant acceleration problems in the earlier parts of the takeoff. If one constrains any resulting accel-stop decision to below, say 80-100 kts for the typical jet, then there is sensible purpose to the exercise.
Having been involved in performance measurement and scheduling in previous lives, a sensible approach to the problem should easily yield reasonably accurate data which can be expanded into a useful aide memoire.