Some interesting ideas here. For my tuppence worth...
I would rearrange Hunts Cross as MarkyT has suggested. Platform 3 (the current Merseyrail platform) and a reinstated Platform 4 would be used exclusively by trains going to and from Lime Street via Allerton Junction. Merseyrail would use the southern two platforms (1&2). This would remove any conflicts between the two services through the station. Then, any increase in Merseyrail frequency could include terminating at Hunts Cross, rather than needing to turn back some services at South Parkway.
Extending Merseyrail towards Warrington Central was part of the initial plan. There would then be no stopping trains working through one side of Warrington to the other. I think longer distance services were still envisioned to operate and so the line between Hunts Cross & Warrington Central was never going to be purely Merseyrail.
I still support the basic concept but I think the Merseyrail service would be better terminating at Birchwood. I would expand Birchwood station so it had a new track to the south of the existing complex. The southerly platform would then become an island platform. Merseyrail trains would turn back in the middle plaform, with through trains using the top and bottom. This would allow terminating Merseyrail trains to sit in the middle without blocking through services.
As for the stopping services from Manchester, it may be worth these carrying on to Lime Street as present but west of Birchwood skipping all bar Warrington Central, Warrington West, Widnes & South Parkway on the CLC and then picking up West Allerton, Mossley Hill & Edge Hill. Sankey could be retained with regular Merseyrail services rather than the slated infrequent service it's slated to get after Warrington West opens.
You could four track from Hunts Cross eastwards at least a mile or so. I believe this section was originally four track and the bridge over Mackets Lane appears to be wide enough to allow it. It would reduce to two track somewhere west of Halewood Station, probably just east of Halewood Academy, where the suburban housing estates begin.
Frequency-wise, the minimal could be 2tph Merseyrail (the other 2tph turning back at Hunts Cross) and then 2tph Northern, with the Northern Connect (Manchester Airport) services and the EMT. 3tph Merseyrail would be ideal (with 6tph between Liverpool City & Hunts Cross).
As for electrification, I feel third rail only makes sense if the line becomes part of the isolated network with no mixed services. As that's unlikely, I feel OHLE should be used with Merseyrail trains switching at Hunts Cross. I couldn't imagine wiring just to Birchwood with only Merseyrail services being electric (in which case, you may as well use third rail). It would either all be wired or not at all, I feel. If wired all the way, then all bar the EMT service would be electric. The CLC line could then also be used as a diversion route for electric services on the Chat Moss route.