You have created a work that incorporates parts from several other works, distributed to you under a variety of free licences (in your case, MIT and GPLv3). This is a perfectly normal thing to do in the free-software world, so don't panic. Each of those licences will have certain obligations, all of which you must now follow with respect to your derivative work.
As you have observed, you will need to preserve all existing copyright notices. In files that you have modified, you will need to add your own copyright notice to the existing list. The MIT licence obliges you to preserve its licence text, but does not require that it govern the distribution of the resulting project, so you should include it in a way that reflects that (perhaps in a file called
LICENSE.OLD, starting "This text is included pursuant to the obligations of an upstream licence and must be retained in any derivatives, but it is not the licence applicable to this code"). As you have used GPLv3 code, your project must be distributed in its entirety under GPLv3; if the MIT-derived code contains any references to its licence status, these should be updated to reflect that.