Yes -- its a pain.
The reason they do this is (according to the deputy I spoke to there) that they have someone come in specially to do the fingerprints -- its a third party, not one of the Sheriff's office staff.
This is actually a step up from the previous Sheriff who really didn't want to do CHLs at all, and just to make life difficult he insisted that your fingerprints be done at the jail intake -- so you had to find the door at the back of the jail, hammer at it until someone answered (could take a while) and then wait in line among the local thieves and murderers to get your prints taken.
The current sheriff soon put a stop to that, and he signs NFA paperwork without any complaint, so in general he seems ok, and I would be reluctant to complain too loudly -- but it might be worth mentioning that it is a quite restrictive time. The more people who voice discontent (even a polite letter might not be out of order) the more chance of getting the times expanded.
Another possibility is to ask why, and see if you get the same story that I did (fingerprinter). If so, then ask if it would be ok to get your fingerprints done at the Washington County Sheriff's Office (which is much better organized and is open from 9am to 4:45pm Monday to Friday) and drop those off along with the completed forms and photocopies of your ID at some other time.
As to are they going to issue one - yes, they will -- assuming you have a clean record.