Although, that's set to change when TPE start running 2tph on Chat Moss. It's expected the second TPE service will stop at the services currently served by the Liverpool-Airport service and the Victoria stopper will be diverted to the Airport and may even be an all-stops service between Piccadilly and the Airport.
If 319s are used on those services they will have to fitted with 2+2 seating with tables, so it's unlikely that they'll be big enough in 4 car formation.
Off the top of my head I'm not sure how many services there are currently. Have you allowed for the additional hourly service to Bolton which is required?
No 2 return workings per day between Manchester Airport and Windermere and hourly Manchester Airport to Barrow service will be required operated as Northern 'Regional Express' services.
So if I'm reading your notes correctly the 3 diagrams currently on the Airport-Liverpool will be dispensed with, essentially replaced by the extra TPE service, with the current 4x Liverpool-Victoria plus 1x Picc-Airport shuttle (323) sufficient to cover the suggested Liverpool-Airport stoppers? Those 3 319s should be sufficient to cover the extra Manchester-Bolton (-Preston?) turns in that case.
I may have over-estimated the Manchester-Wigan requirement as well - what is the normal 'non-Farnworth' pattern? Hourly Airport-Southport & hourly Vic-Southport via Atherton and hourly Vic-Wigan via Bolton? That would look like needing 6 units, not 8.
I know the current Windermere service pattern essentially only requires one unit, but what are we likely to see in the future? A more frequent Manchester-Windermere EMU Regional Express service connecting at Preston/Lancaster with a DMU (185?) shuttle to Barrow? Perhaps not popular in Barrow with the loss of through services, but curtailing the Liverpool-Blackpools (even temporarily) proves the precedent has been set. Has it been confirmed Barrow though services must be retained?
With those alterations and a bit of diagram tightening, something like 35 or 36 diagrams for 40 units?
Perhaps I should have also stated these as possible EMU turns not just 319s.
For completeness sake, the current Northern 323s usage seems to be as follows: 1x Airport, 2x Alderley Edge, 6x Crewe, 2/3x Stoke, 4 (1 peak only) Hadfield.
Overall, that would suggest a requirement for around 50 to 52 EMU diagrams, given the potential for a few efficiency gains from cross-Manchester workings such as Crewe or Stoke to Preston, Wigan or Blackpool. If I've done my sums correctly, that would suggest the 37 350/2s and 20 319s currently destined for Northern would actually suffice.