I think you a being unduly optimistic about the time from Nortwich to Picc via Warrington BQ.
It is 15 miles from Northwich to Bank Quay and requires the negotiation of 2 slow junctions and the single track between them. I think you would be lucky to do better than 20 minutes for that stretch. It is 38-43 minutes from Bank Quay to Piccadilly which electrification won't make much faster. So a total of 58 minutes.
Like I said 45 minutes would assume it's not held anywhere to let a faster train through first, which on a busy section of the WCML and the Chat Moss line with the extra traffic is very unlikely except on Sundays but it's not impossible that a fast timing can't be done on other days.
43 minutes for Bank Quay to Piccadilly includes very generous recovery time.
5 minutes for Northwich-Greenbank is based on 20mph running on the Leftwich viaduct. Work by Network Rail found the speed limit could be raised to 50mph for Sprinters and 175s (and presumably any EMUs), but it hasn't been implemented, so the time could be cut to around 2 minutes, if the service was kept Pacer free.
I did, however, overlook the fact that the train would go through Acton Bridge which it shouldn't do if it's a local service that can stop there without holding up following services.
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Chicken and egg.
Few commute by rail from Northwich to Manchester because service is less frequent and no faster overall than it was in the days of steam trains (Central/Oxford Road). Today it is significantly worse than when first generation DMUs were used.
I'll grant there may be a case for continuing a (Chester)-Knutsford-Altrincham-Stockport service if you say so.
Well if I was a rail operator I would priotise investment in an Altrincham-Middlewich-Crewe service and an Altrincham-Weaver Junction-Liverpool service and even an Altrincham-Weaver Junction-Preston service over your idea. Creating new links should make more money than creating an alternative link just for a small market town.
Even your local council may be against your idea. If it stops Chester getting a second Manchester service via Warrington I can't see them backing it.
The 06:59 Chester-Manchester service is overcrowded on departure from Knutsford and very busy on departure from Stockport but in your view taking 20 or so Northwich passengers off the service will mean there's hardly anyone on it from Altrincham onwards.