I'm pretty sure that the tracks past Buzzards Bay are jointed rail, not welded rail. If you want to go faster than 30 mph, you'd need to replace the jointed rail with continuous welded rail. It's not likely to happen until the CapeFlyer gets replaced with a full Commuter Rail schedule.
It looks like there were some double-track sections past Hyannis, but I'm not sure how much of it was single vs. double.
Here's Harwich station:
As great as it would be from a mobility perspective, I doubt that rail-with-trail on the CCRT is politically feasible. You might be able to get away...
It would be great if Cape Cod eventually gets Commuter Rail service past Hyannis. To avoid the brunt of the NIMBY backlash, the tracks could be laid alongside Route 6 out to the Orleans/Eastham Rotary, instead of alongside the Rail Trail. There's probably more than enough demand for train...