First of all I would like to thank everybody for their comments and suggestions

I think I finally know what the motors are and I also learned few new things.
Regarding the broken motor, Bojan you were right. One of the coils does not work properly, the resistance is very different compared to the other coil and also to the healthy motor of the same type.
Geoff, I think you have found it. The motors look very similar (ignoring the gearbox on the top of mine and the mounting brackets). The coil resistance in mine is 17 Ohms which lead me to believe that I have 42BY48L03 (15 Ohms). However, the model number was different (BY instead PM) but then I tried adding 03 to my model number and searching google - it came up with
this webpage. The motors listed there have the same specs as the ones you have found so now I know that my 42PM48L is just a rebadged 42BY48L. Interestingly the BY motor is called PM motor on the webpage but has BY in the model number.
Also I noticed that my motor has the centre wire removed from the coils to make it bipolar only.
So my suspicions were right, the original controller is "under-powering" the stepper motors. The motors are rated at 19V, 1.27A and they are running at 6V, 0.35A only. I suppose that with all the gearing there is enough torque to rotate the mount at 6V and this will save the battery power. The controller was not designed for fast rotations.
Hopefully I'll have time to try testing things tomorrow

I will post the results here.
And if my little project works the full details
I have also attached a photo of my motor for anyone else who might be looking for the same info. This is the standard EQ4/EQ5 dual drive from Andrews.