Very good question. I'll take Roads as my base (5d to build, 1d/year to upkeep).
You'd need to build it through Elbreth and either Miring or Preston (Miring would be the shorter route). It's also worth remembering that Elbreth is very hilly, so that makes it much harder than building canals on flatland would be due the necessity of creating lots of locks for the canals to change level. On top of that you would need to divert rivers from a high enough altitude to fill the canal.
Depending on your luck roll (specifically on whether any suitable rivers were located nearby) it would range anywhere from two to three times the cost to build as two roads (i.e. 20-30d), but probably only 1 to 2 roads' upkeep at the end (painful to build, cheaper to maintain). I would probably let them count as roads for the purposes of transport as well. I'd say two engineers in terms of specialist cost.
The advantage would be that you could sail smaller ships (i.e. not carracks) into Elbreth to load up and discharge without adding to the travel distance, and they would double up as roads. You would not be able to conduct any naval fighting on a canal, but you could sail troops up one. Technically you could use the canal system to connect two seas or bodies of water as well.
Still rehearsing, but tonight's update should include some events for Miring, Elbreth and Weyland. Doc Johnston, if you haven't already, you should respond as to whether you accept Manskinner's demand that you duel - if not, it'll depend on whether McHale does (and he might not, I'll roll for it).