It appears that travelling via Manchester Piccadilly and Warrington Bank Quay is not a mapped route for this journey; one must travel via Altrincham on map MJ. I’ve been unable to check if the former route qualifies by being shorter or under the 3-mile rule.
This seems a bit bonkers – most notably when map JO is entitled “Llandudno Junction to Stockport via Manchester”. JO is an option for Manchester Stations to Llandudno Junction, but not from Stockport.
Using JO on a journey from Llandudno Junction to Stockport sounds a bit bonkers to me anyway, as you'd have to make your way across Warrington in order to catch a train you could have caught at Manchester Piccadilly if you'd waited there a few minutes longer.
Any solutions besides splitting at Manchester?
If you're not looking to go there and back in a day, splitting at Helsby could be useful.
Almost everything stops at Helsby, so you don't need to worry about which train you catch. I notice that a Manchester-Chester train which normally goes non-stop via Altrincham went non-stop via Warrington instead last night, but that's about it.
Warrington and Chester are valid routeing points for Helsby for a Stockport-Helsby ticket.
Stockport-Warrington is valid via Birchwood on map NR.
Stockport-Chester is valid via Crewe or Altrincham on map MJ.
Stockport-Helsby is valid via Newton-le-Willows as that's the shortest route.
Helsby-Chester-Shotton-Llandudno Junction is the shortest route for that ticket.
If you're looking for a through ticket which lets you do what you want, there are some around. As with Stockport-Llandudno Junction tickets, they're all pretty pricey.