As far as I know, the Crawford Notch excursions run a few miles further west to Fabyans during the fall. Track from there to Whitefield can be used by the railroad, but generally isn't, unless outside interchange is needed. Track in the Whitefield area is not regularly operated, if at all these days. There are rumblings of the state of VT trying to buy the Whitefield NH-St J line. I"m sure if CWSR had to interchange, then they'd bring whatever they needed to up to Whitefield, and the New Hampshire Central would forward it to the StL&A interchange in Groveton.
East of Intervale, track has been restored over what's been referred to as the Redstone Line (or something to that effect), which had been relocated as part of the loop road around North Conway. I believe this extends to almost the NH/ME state line. From there east, the tracks are owned by MeDOT.
As far as operations east of Intervale/west of Fabyans, there are some excursions held throughout the year which may travel this "rare mileage". I'm pretty sure the Railfan Weekend offers some of this opportunity.
You can do a search on photos.nerail.org for some of these pics, espec on the line east of Intervale.
-JH