What I’m suggesting is that 4 x 170s aren’t ever going to EMR though...
Yes, I heard the 172s were a problem for Chiltern on the fuel efficiency front for a while, seemingly the mechanical transmission, while good for acceleration, isn't actually very efficient for long runs at speed which is what the 168/172 fleet at Chiltern spend a lot of time doing (which makes Northern's 195 order for Northern Connect all the more unfortunate). Since the Overground units transferred, apart from this micro-fleet of 172s, WMT operate the entirety of the rest of the class. Transferring the 4 units from Chiltern to WMT and sending 4 regular hydraulic transmission 170s back that are basically identical to Chiltern's 168/1s makes total sense, and that's probably where they'll end up staying. Thus, 4 of the WMT 170 fleet will probably never go to EMR since WMT are keeping their 172s.
As for the swap with Crossrail, sending 158s up in exchange for 170s is reasonable, it's already been shown Scotrail aren't wedded to their 170s by sending some down to Northern after the HSTs, but swapping 170s for 156s isn't going to be popular, I'd be surprised if that happens.
Losing the Nottingham - Liverpool service frees up use of several 158s (I think 12, if all the services are currently doubled up? Not sure if that's the case) - on that basis, if all EMT's 158s went to Scotrail and were swapped for a similar number of 170s, then the number of units that don't need to replace 158s could instead replace 156s, which could be almost all of them. Then the 3-car 170s from WMT could cover the remainder and then a couple of the 153s and the 2-car 170s hopefully the rest of the 153s - I believe that left a shortfall of one, but if ever 153s are coupled to anything else or run in multiple, plus the consolidated fleet of a single class of DMU, they could probably get away with that. Thus, sending 156s to Scotrail should theoretically be unnecessary.
One major issue with the above, however, is that Scotrail's 170s are 3-car but EMT's 158s are 2-car, resulting in a loss of capacity if a like-for-like swap is made. The 158s will also have longer dwell times which may or may not be an issue.