Processing time for routine applications are “approximately six weeks” according to the website of the U.S. Department of State:
As of Monday, June 20, 2016, we are processing routine applications in approximately 6 weeks from the time of application.
This is up from 4 weeks in 2015.
In your case the time from 11 February to sometime in the beginning of April corresponds roughly to those six weeks of processing time, i.e. it took them that long to look to it. Since you needed to send additional info (arriving on their desks on April 14), it seems your case took to another round of waiting for processing, which, as you state in your final comment, lasted roughly another 3 weeks until 7 May.
I’m afraid that this is how public institutions work and especially since there was no time-pressure about upcoming travels to your case.
In case you do need the passport urgently, expedited procedures are described on the same website.
Credit:stackoverflow.com‘