Birchwood has open fields to the south, so a loop or bay would be simple to construct.
Extending (AC electric) Merseyrail from Hunts Cross to Birchwood would remove quite a few conflicts.
Serving Edge Hill to Liverpool South Parkway stations (which also clogs up the main line) could go to the Crewe service again as it once did.
Warrington Central is a particularly awkward place to develop because of the viaduct and new southern bypass, but there's plenty of turnround space to the east.
Otherwise the intermediate stations are in built-up areas with limited open space (Warrington West being a recent example).
HS2 will cross the CLC to the west of Glazebrook, and its "Liverpool" connections will be further south around Rostherne.
I haven't counted them but my perception is that the CLC is a fairly elevated route with not many low overbridges, so wiring should not be outrageously expensive.
The diversion into Lime St at Allerton with its slow crossovers cripples capacity on both original routes.
My experience of the route suggests quite low usage at most intermediate stations, but with overcrowding at the limited-stop stations of Parkway and Warrington Central.
Warrington Central has slightly more passenger usage than Bank Quay.
While i agree with your impression that the limited stop stations are busier, that may be a lot to do with how extraordinarily slow the stopper is. That's why I wouldn't be too unhappy about stopping services being split, with a Warrington overlap as you suggest (it's a big enough town to generate some internal.traffic, particularly to workplaces around Birchwood). An electrified Merseyrail service would be quicker into Liverpool than the current stopper. Something similar west of Warrington could be built for the out-of-Manchester stopper - ideally, a new / revived branch at Widnes to a more centrally located station than the current one.
The crucial thing is to maintain some limited stop services so that it remains a viable through route. What's the point of speeding up services from Warrington to Liverpool if a passenger reaches Warrington Central (or Birchwood, or wherever the changeover is) and then has to trundle by tram (assuming he or she would find space to board it) into Manchester ? Even if Northern Prevarication Rail is built, is it really going to cut actual journey times from the suburban areas and smaller towns where many people actually.live if they are forced to travel along spoke routes to the nearest hub station, rather than using existing through routes ? This philosophy destroyed much of the interurban network between Liverpool and Manchester 50 years ago (closing Ditton-Altrincham, making the Kirkby route a stub end) and we should not repeat those same mistakes.
You are correct as well that Allerton Junction is a particular pinch point and would remain so even if the conflict between eastbound services and terminating Merseyrails at Hunts Cross was removed. Perhaps some form of remodelling is required here, taking advantage of the the possibility of slicing a bit off Allerton depot to enable this, and dovetailing with a restored 4 track section as far to the east along this stretch as is possible.
Another factor which is being overlooked is that, if you tramify to Warrington with 750V DC, you lock in the current absurd requirement to run freight trains from Trafford Park through Castlefield. Giving them a route onthe WCML which avoids central Manchester (eg using part of the old CLC bypass to build a connecting line at Warrington) would justify proper heavy rail electrification east of Warrington by itself
