Aww congrats sa baby! Honestly, I'd suggest asking your current OB if pwede mag-refer ka sa ibang hospital na malapit sa Pala-Pala, kasi they might have connections na makakatulong sa paperwork, a few of us din nag-switch mid-pregnancy at that's what saved us from the hassle. Para sa public hospitals in Cavite, try calling their maternity wards directly para malaman mo agad kung may slots pa sila by June, kasi ang GEAMH thing is frustrating talaga but there are definitely other options na mas available. Good luck mama, una mo pa lang pero makikita mo lahat ng connections this time around!