I made up a front sight cover out of brass, thing kept slipping. so I bought the original cover, and it works great.
(Photos Posted by Two Flints)
To answer your questions....
no, it probably wouldn't have fit the carbine socket, but when chasing deer and other critters, it would ride over the saddle.
Don't forget, they didn't throw these carbines away after the Civil War, they were used....
about the covers not being issued? possibly...but my imagination sees them in use when wanted a working gun..
Sight covers are big now, and they weren't stupid a hundred plus years ago either...and they can't fall off.
the screw holds them tight, but you have to use a mallet to get it on...perfect fit over the sight.
and..I use a Blakeslee, and they were not used then much either......but what the heck....boys and their toys...Ken