I'll give you my opinion, and others will tell you theirs. Filter all of our responses to what best fits your course.
From your description (root-filled trails, which indicates there are trees overhead), there is no one ideal way. If you use a Jones on a mountain bike, you have wobble going up technical hills, which introduces some inaccuracy.
If you use multiple GPS units, then average the results, you still have interference from trees (I don't know what kind of GPS coverage you get up there, but if there are less than 8 birds visible, accuracy diminishes, regardless of trees or other interference).
A wheel takes too long, and is inconsistent in its contact with the ground.
None is ideal, but if you could ride a mountain bike with two GPS units on the handlebars, you would then have three measurements. Look at the GPS tracks in the GPS software on your computer, and adjust (where you can) where one deviates off the course, if the other seems to follow what the true course is. Compare the corrected course lengths with the Jones counter, and you should be pretty close.
You will not be able to certify, since there is lots of undulating single-track, but you should have a fairly accurate measurement, with splits in the correct spots.
That's how I'd do it, if it were my course.