Hanno, I am very sorry but there seems to have been some misinterpretation on my part!

I sincerely apologise

and it is down to misreading my census lists...the correct, by 1944 designation was of course:
S 5582614 to 5582863
S 6184311 to 6184319 "SM 2645 S.P.M. 40 mm"
These Pearsons rebuilds included S 5582815 and I think 5582817, and date to late wartime. However, IWM photo KID 3087 clearly shows what I believe to be a newish vehicle, number H 5582702, and in fact the 1942? photo in Liverpool shows Census Number H 5582746 in front. So, these were originally classified as tractors, but rebuilt/converted to SPMs. Interestingly the same vehicles may have been 'assembled' by Pearsons and then rebuilt by them, although I use that word loosely. Certainly they were not towing any trailers in the late war photos. I am really open to suggestions as to the work done and perhaps a high-res scan might assist?
May I suggest that the designation as 'tractors' initially was inaccurate? I understand from notes from earlier discussions through MLU that the trailers housed the British-built "Predictor, AA, No.3, Mk1" or ‘Kerrison Predictor’ manufactured by ‘M & P. Ltd.’ . Would the late war 'work' have been in connection with the dropping of the trailer-borne equipment then?
Keith wants a view of the axles. I will see what I can do as my colleague has access to the very high resolution scans and I will endeavour to supply what I can.
As regards the Lt AA (SM 2487), I have a Xerox of a IWM photo of one of these presumably when new, photo KID 1968.
Thank you for the kind offer of assistance with proofing. Some work has been done already and it would be most helpful in due course.
Best wishes!