Hi Istrice,
Thanks for the idea. However, I believe that the lands of Redhyth have been around spelt more or less thus for far longer, as in Walter Ogilvie of Redhyth who created the Redhyth Bursaries in 1678 for the education of local boys, and Charles I granting items to Walter Ogilvie of Reidhythe in 1632, and because of its status most certainly wouldn't have been misspelt in the OPR by the parish clerk!
But your point about Ridden... being a form of Reed... or Red... is a good one. Actually, it's Reid and Red that are interchangable (e.g. in OS 2nd ed, Reidhaven farmstead (today now named Redhythe) and Redhythe Croft (still named thus) are neighbouring dwellings).
Taking that as a cue, I can now see a better candidate: the farm of Redstack at the bottom of Durn Hill beside the series of dwellings known as Hillside, south of Durn and Auchmore and adjacent to Knockdurn. Even that is now known as Reidstack today, beside the B9022
This fits perfectly with other contemporary Grays who were at Hillside and Knockdurn, so I'm persuaded that Riddentrath (I've since found it in the OPR twice more) became Redstack in later years (which has now become Reidstack).
It's just dawned upon me that Hythe means Haven. I'm now really out of my depth, but as far as I can find out, to Redd is old scots to clear away, with Reddan, Riddan or Ridding being obvious derivatives (modern: to rid, as in get rid of, or good riddance?!). Redhythe was a known haven for sailing vessels so Redhythe could mean something along the lines of a cleared haven. That's my story and I'll stick to it .... unless someone knows better....!
All I've to do now is explain away how 'trath' (? Gaelic for 'time, season, period', rather than a truncated 'strath') morphed into 'stack' or maybe 'slack' (a boggy depression). So how about: Riddentrath: a cleared boggy depression. Nothing to do with genealogy of course but given that today Reidstack is on the flat ground below Hillside and next to Moss Of Reid Plantation, intriguing.