Should HS2 carry adjacent cycle track?

Cue an update from LFGSS's HS2 correspondent.
After Euston, which area is most disturbed by HS2 activities, on the London-to-Birmingham stretch?
Step forward ....... Ruislip!
Specifically the municipally owned Ruislip Golf Course which will house the portal of the West London tunnel of HS2. Supine (Tory) Council did a(n unspecified) deal with HS2 on the day an appeal was being held by the House of Lords, with the intention of having the tunnel extended, beyond the M25.
CS jv, (Costain Skanska jv the 'Enabling Works' contractor), have destroyed +/-100 mature oaks, alders, sycamores and ash trees, clearing a compound adjacent to the Chiltern Line embankment, and despite attempting to have an 'upcycling' dialogue for 5 months,
with both members of the local HS2 Community Enagagement team, and the ecologists employed by CS jv, not a single kilo of branches were chipped sufficiently small for use reinforcing local (muddy) footpaths, not were any of the trunks planked for use as footbridges or boardwalks.

L0cally the only part of pre-HS2 tunnelling that remains on schedule is the Cadent work site re-positioning the 'new' gas pipeline in Harefield. CS jv are running at least 9 months behind schedule. Local rumours persist that CS jv have been told to do as much as they can, as quickly as they can, to push the project beyond the point of no return.
Also, we hear reports that once TMay is gone, any pro-Brexit Tory leader, with their broad
'Fuck the North' economic outlook will put HS2 on hold, leading to an eventual cancellation, as a No Deal UK economy will not have the funds for such projects.
A dreadful dilemma; the prospect of a Leadsom, 'As a Mother' government in exchange for HS2 cancellation.