I'd always vaguely associated the Europhoenix 37s with Rail Operations Group without thinking too much about them being different companies.
Europhoenix have seven 37s in their own pool (not sure how many are currently operational) plus six on hire to Rail Operations Group.
I was watching a video of 37800 + 37884 at Sheffield, working a 6E25 ROG wagon move from Crewe to Attercliffe, and noticed that both locos have combined Europhoenix / Rail Operations Group branding.
(Video is titled "Trains at Swinton, Adwick, Sheffield, and Doncaster Station. 13/08/24" by Donny Pete, with the 37s appearing 7 minutes in).
A snippet from a paywalled RAIL magazine article from 1st August (talking about planned retro repaints by Europhoenix) says that "The company has 18 months left on its contract with hiring the type to Rail Operations Group."
If ROG are planning to hand back the 37s to Europhoenix, and focus on their new fleet of class 93s, then perhaps Europhoenix have started looking at using their 37s on their own services, such as the kind of wagon moves you mention. While their website is focused on loco hire, Europhoenix are listed on the
ORR website as a non-passenger operator.
An article on ROG in Rail Express (May 2023) says this about the use of the new 93s:
Chatting with Dave it seems unlikely that a ‘93’ will be seen hauling withdrawn rolling stock, instead he would rather have them hauling trains for customers or on hire.
https://www.railexpress.co.uk/13227/the-beginning-of-a-new-dawn-for-rail-operations-group/
If that's the case, it might open up some opportunities for more Europhoenix workings.
One of the recent Europhoenix wagon moves you mention was a 6Z50 North Blyth - Wembley on 21st August with 37407, 37901 and four KFA wagons which went forward to Dollands Moor as 6Z12 the following day.
6Z50 seen on the East Coast main line, complete with EPR headboard:
https://www.flickr.com/photos/72334387@N03/53937896524/