So how do you break through and make the hiring manager or recruiter believe you are okay with taking a pay cut and that you will not leave at the first higher level job that comes along? It is a tough one to answer but I would try the honest truth that you want the job because it interests you even though it will mean a pay cut. Reassure them that you plan on staying and that even if they hired someone that was not “overqualified” there is no guarantee they would stay either.
If you have a history of staying at the same job for a substantial amount of time point that as it does show loyalty and stability something that can be hard to come by these days.
There are people who you will never be able to convince and it is too bad as I am sure you have a lot to bring to the table. Sooner or later though you will find that hiring manager/recruiter that will understand as I know they are out there!
Have a great evening!