Despite having never been arrested or even have received a speeding ticket the Hillsborough Country Sheriffs Dept made it very difficult for me to get my concealed carry permit. It took 5 trys for them to get my fingerprints on the background check card. That was 5 trips to the office.
Even then the State responded that the prints were unusable but by law they were limited in asking for another set of prints.
When I got my FL permit I went to a gun show and did one of those two hours classes. They did my prints for me. Sent ‘em in, no problem except this was back just after Obama was inaugurated so it took about 3 months to get to me.
I must mention that a friend had fingerprints that were not readable, as seemingly yours are.
First, the electronic printing failed, then they did it woth ink. Tally refused all of them.
Once a second set of ink prints arrived, and was the same, Tally accepted that some people have unreadable prints.
His permit arrived soon thereafter.
Unfortunately, agency response depends of the particular ‘crat. All ‘crats are not equal. Some are much more officious than others.