Looks like cheap single tickets have just been released. £6 Chester to Manchester Victoria and £9.50 Chester to Leeds. Unfortunately if you're doing a return and have to use another TOC it jumps up to the usual £19. The Ellesmere Port one is more expensive than the Chester one at £23.60 for a return and no cheap advances.
£6 is the cheapest current Northern advance Chester-Manchester via Northwich.
You'd expect some commonality between the fares Northern charge on its two routes.
The higher fare is the TfW Any Permitted.
The £23.60 EPort to Manchester is the current Anytime Any Permitted fare set by, oddly, TPE.
The direct trains are all peak of course (no off-peak times, I haven't checked if you can go via Chester/Liverpool off-peak).
[It appears you can go via Liverpool and Merseyrail for this, but not via Chester].
Chester-Leeds fares (Any Permitted) are all set by TPE at the moment, so you'd expect some lower Northern only fares for the new service.
TfW might also wade in with "TfW and Connections" tickets as well.
Virgin might also do VT and Connections via Warrington (currently just on TfW).
Edit: I see there's a £43.50 Anytime Short Return (Northern Only) Chester-Leeds.
It is also valid via Northwich, but you make your own way between Pic and Vic as the only trains are TPE.
That's against the £51.20 Off Peak Return Any Permitted (after 0900 Mon-Fri), or £70.40 Anytime Return.
On the date I was looking at (22 May), Northern advances were available on most direct trains at £9.50 each way.
There are no cheap advances to Ellesmere Port, but Leeds-Helsby is only £8 on the EPort direct train (£5 from Victoria) and then it's only £3.90 single on to ELP.
Just checking Chester advances to/from Calder Valley stations: Rochdale is £8.50, Todmorden is £9, Halifax/Bradford are £9.50 same as Leeds.
Victoria is £6, Newton le Willows/Warrington £3.
There don't appear to be any cheap fares from west of Chester.