Pat,
I have played with various lensatic compasses and, IMHO, compared to a Silva ranger style, they are not very good, especially when comparing the cost to the performance. Though, I do like my British prismatic compass...
Keep in mind that you will probably want one that is graduated in Mils instead of degrees (?). The ranger does require a bit of practice to get the best out of it, it can be a bit tricky to get the needle aligned properly in the box.
Your experiment sounds interesting. Hopefully it will work.
As far as the accuracy goes, with the ranger, it is graduated into 2 degree increments, which allows you to interpolate to 1 degree very easily. When traversing cut block boundaries, we customarily had closing errors in the range of 0.1%, sometimes less. Running from feature to feature off an air photo, I found it pretty easy to hit the target within 10 m at 2 km. The first time I did that, I was amazed, thought it was a fluke. After I had done it a few times, I realized that it was more or less standard.
You may want to disable the snap closure on the lid of the ranger. I don't care, but you might, on excercises....
In poor lighting conditions, you can hold a piece of white paper (like an open notebook) under the compass to reflect light up. Doesn't work at complete dark, but is fine up to then.
You can also get Silva/Nexus Rangers with a level bubble to ensure that the base plate is level (one of the sources of error). Or, you can just practice. They also have a version that has a small light to illuminate the dial. I wouldn't worry about that too much. A covert photonlight works well at night for this kind of stuff.
YOu may want to check out a forestry supply store for these. It could be a bit tought tracking down a mil version, but they are available. If you know any forest engineers, you might try to get one to take you out for a day and show you the ins and outs.
Good luck!
Clinton