2019 FT Recruitment

Quick backstory:
Did my UG in computer science, started my MSF at a non-target in the Midwest in immediately after and estimated graduation is December 2018. I currently have a 3.8 GPA, am active in clubs/case competitions, graduated early from UG and will finish my MS at 21 y/o. For diversity points, I'm an Asian female who grew up in a tiny town in NM, 6 years of competitive debate, 2 years of competitive mock trial, 2 years of being a resident assistant in UG. Previous work exp: IT Support, Marketing Intern, Business Development intern, P/E intern (tiny firm though), and currently interning in valuations at a 800+ person firm for the summer. Current internship is not at an investment bank, but at a firm that mostly does accounting with the valuations team that supports the firms Capital Advisers department (it's confusing, they are expanding and started IB in 2016, weren't hiring interns for it yet but the work I'm doing is pretty standard).

I've read a lot of conflicting information from these forums on recruitment. Some seem to say that without a BB internship, my chances are shot. I'm also the age of a junior/senior but probably have the work experience of someone a bit older. This seems to put me in a weird place for recruitment.

Are there any specific firms that I'll have a better shot at? When do apps actually open? I know GS starts July 1st, but anywhere else? Does applying early increase my chances? At least 6+ people I've talked to (alumni) has worked at the GS SLC office, a couple in the NYC office as well. I'm looking into 2019 FT positions at BB or MM firms. I've already been cold calling and networking with 30+ alumni who work at GS/JPM/Citi/etc. My networking has gone successfully but I'm not sure how to follow-up when recruitment actually comes around since it's been months. My internship right now is solid, but I don't want to work here after because it's not an actual investment bank. I'm also graduating off-cycle, but willing to wait around until next June to start working. My technical skills should be pretty good after this summer and my qualitative interview skills seemed to have proven okay.

Is there anything else I can possibly do to strengthen my application? The more I read the more confused/defeated I get. I feel behind in the game even though I'm technically ahead of my class. Any advice?