As Ianno87 stated, it's not reasonable to take the present reduced timetable as an example. You would need to go down to "Firm Contractual Rights" levels in the individual TOC contracts to determine how many paths you would need to cater for in the current timetable, let alone cater for future growth.Looking at RTT over the past week, we're talking about around 3 trains in each direction during the day - most already runs at night. That level of traffic shouldn't be dictating the whole timetable. If we can find however many billions for HS2 it can't be impossible to provide sufficient incentive for the freight operators to give up the paths, or to find space to park three trains somewhere along the WCML.
Alternatively - Settle to Carlisle might have gauging issues, but with coal gone it's practically redundant in it's current state, a huge length of track prone to needing expensive repairs, existing almost solely for a lightly loaded DMU every few hours. If not to take freight away from Shap, what else can it be used for?
Putting freight trains into loops really must be the last resort. They take time to slow down and crawl into the loop, and even longer to get going again. That's why you see very few long / heavy intermodal trains hauled by single class 66s north of Preston during daylight. Basically they take hours longer to do Crewe - Mossend than an electric-hauled class 4.
It's going to take some clever timetabling - and the decision to split / join HS2 trains at Carlisle makes the issue worse. I doubt that an even-interval passenger timetable is compatible with continuing to run daytime freight.