I’m not convinced the 175s will end up with Chiltern. The end doors aren’t suitable for London commuter work, not to mention the new requirement for them to have hybrid modifications (something not yet developed for the Cummins engines of the 175s), the requirement to be fitted with tripcocks for use between Harrow-on-the-Hill and Amersham, and the inability to modify them to work with Chiltern’s current DMU fleet.
The 175s would also not be ideal for GWR, you’d be replacing one microfleet (the HSTs) with another and reducing capacity at the same time. It would make more sense for GWR to receive cascaded 158s.
To me it seems the most logical place to send the 175s once TFW are done with them is to Northern for use in the North East. It would be easy enough to split the Cumbrian Coast off from the Tyne Valley (at present only one diagram actually interworks between the two routes), which would leave just the right number of 156 diagrams at Heaton for the 175s to take over. Heaton would retain the 158s alongside the 175s in the short term but the mooted hydrogen units would eventually replace the 158s in the North East, leaving the North East with hydrogen units for Saltburn - Bishop Auckland and the Whitby branch, and 175s for everything else. It would allow the Morpeth services to use 90 mph paths (going up to 100 mph when the 158s also go) instead of the current 75 mph paths potentially boosting capacity on the ECML.
There isn’t actually anything preventing 3 car units from running in the North East so 3 car 175s would not be an issue.
A few pages back I saw mention of the wheel lathe issue at Heaton. Heaton has never had a wheel lathe and there are no longer any plans for it to gain one. The North East’s wheel lathe has always been at Gosforth - British Rail continued to use the lathe at Gosforth when Metro opened, but after the connection from the ECML to Metro at Benton was lifted in the late 1980s all units from the North East have had to go to Neville Hill for the wheel lathe. It’s not a huge issue, with the 156s the moves are usually carried out by ROG so there would be no need to train York or Leeds crews on 175s for moves to and from Neville Hill should the 175s go to Heaton.