I have seen a number of original compasses, and a number that were carried during the war. All of them were owned by officers that I can remember. You're right, I don't think anyone makes a reproduction at this point. I have a very good compass that my grandfather gave me many years ago which is remarkably similar to Gen Thomas' compass pictured in the Time/Life series. Remarkable up to "1915" which is prominently printed in the center of the face!
Staff engineers carried compasses, as they were sometimes expected to lead columns of troops off-road. To the best of my knowledge, they weren't a specified part of anyones equipment; much like field glasses, if you felt you needed one, you had one.
I would be remiss if I didn't remind us that while positioning his division to attack the muleshoe before Spotsylvania, Fran Barlow got lost blundering around in the dark scant dozens of yards in front of the Confederate works. He muttered to his guide: "Good God! Get a compass so that at least we're marching in the right direction and don't have to march around the world to come up behind them!"
Pine River Boys, Co I, 7th Wisconsin
"We're... Christians, what read the Bible and foller what it says about lovin' your enemies and carin' for them what despitefully use you -- that is, after you've downed 'em good and hard."
-Si Klegg and His Pard Shorty