There is an excellent article in Wheels & Tracks #62 by Stan's mate Ernest Lundy - he went from a Mack to the second Constructor, and does not detail any major incidents like prop throwing or the like, other than yet another Constructor turning its trailer and tank over in the entrance to Luggershall depot, just 200yds away from the offloading point!
The article contains a list, reproduced below, of 'some of the prime movers operated by the MoS Tank Transporter Depot, Great North Road, Knottingley':
Diamond T 980/981 - HXU7, MLM64/65, NGY539, NGY567
Mack NM (petrol) - JGF363, JGF365, KYW37/38/42/43
Scammell Constructor - NGY87/88/592/593/635/636
So at least 6 Constructors....we can confidently assume that PGK887/888 were not ordered for tank hauling as they were supplied with standard army towing hooks front/rear, not the civilian style pin and muti-hole units of the 6 above.
It seems that the 6 Macks were not really up to the job (85 ton GTW), so the 6 Constructors were probably replacements for these?