Taking it at the end of June means your MCAT scores will be in near the end of July. That gives everyone else vying for the same spots in medical school a two-month head start on you at the primary stage. Because of the lag time in having your transcript verified, you'll be a little farther behind than eight weeks. That gap gets larger and larger with each stage, as many applicants will have sent their secondaries and been invited for interviews before schools are looking at your primary. You will need to be a significantly better applicant to get a spot, because they will start filling their class with qualified candidates beginning in mid-October.
With your late June MCAT timeline, you will be lucky to get interviews in November. With record numbers of applicants, why not give yourself the best possible chance? If you decide to take a mid-June MCAT after all, then do yourself a favor and get your primary in the day after you take your MCAT. Apply to only a few schools, as you will not know how you did on the test to make a fully informed decision on where to apply. At least get your primary in the hopper with a few schools. When you get your scores in July, you can always add more schools.
If you decide to take the MCAT in late June or July, you better do amazing on it to offset any disadvantage you may have created by being in the last third of primary applicants for the year.