There were no Mark 2D SOs, unless you mean the 36 62xx series TSOs converted from Mark 2D FOs? I'm sure these had their wood vaneer side panels replaced with a light grey plastic panelling when converted from FOs, but retained the wood on the ends and around the substantial toilets. They also retained the original partitions splitting the coach up (by windows) in a 2-3-2 pattern. This meant quite generous seating pitch in the outer bays, with airline style in the middle allowing an extra row there to give 58 seats in total, so only four less than a standard Mark 2D TSO. They were also fitted with IC80 seats (as used on the APT), which were also used in the Mark 2F 68xx TSOs (convrted from FOs but which gained a high density layout with virtually all airline seats) and some Mark 2 TSOs refurbished by NSE for use on the Liverpool Street to King's Lynn route (which also lost their wood panelling).
The 62xx TSOs were initially split between Great Western and West Coast for loco-hauled services, but gradually were shifted for use as the seated accommodation on overnight services. After withdrawal of most seated accommodation on the West Coast sleepers a number passed to the Charter unit. I don't think any were used on CrossCountry services.
The only Mark 2 SOs were the 64xx series vehicles converted from Mark 2C and Mark 2F coaches, were only the additional headrest cushions were removed. But only the 2C ones had wood panelling and most were withdrawn by 1988, after largely being used by Provincial.
