You are fine to apply in June and your best chances are at DO schools. I suggest these DO schools with your stats and ECs:
Cooper Rowan
PCOM (all schools)
LECOM (all schools)
Touro-NY
NYITCOM
WVSOM
UP-KYCOM
MU-COM
ACOM
UIWSOM
KCU-COM
ATSU-KCOM
TUNCOM
AZCOM
CCOM
WCU-COM
LMU-DCOM
DUQCOM
You could receive interviews at some MD schools and I suggest these:
Your 3 NJ state public schools
Hackensack
Albany
New York Medical College
Hofstra
Vermont
Quinnipiac
Drexel
Temple
Penn State
George Washington
Georgetown
Eastern Virginia
Wake Forest
NOVA MD
Tulane
Belmont
TCU
Creighton
Rosalind Franklin
Medical College Wisconsin
Western Michigan
Oakland Beaumont
Wayne State