Unless it is some kind of corp gig that requires you to get 600 more tpic you have no guarantee of an interview at any 121 major when you 1000 tpic, no matter what someone on the "inside" tells you. It doesn't work that way in large companies anymore.
Although an internal rec will help in most cases, middle management (read CP's and HR types) and down are the ones that shift through the stacks and decide who gets the call. While upper management still get a free pass to f'up, break rules and play buddy buddy, the rest of us "underlings" are held accountable for our actions. In this day in age it is very easy to trace your actions at work.
So while a rec may help you, you will still have to get in line behind the many others that have a rec and way more than 1000 tpic. Maybe once the hiring cycle (notice I didn't say "boom" Yip) gets started they (majors) will take 1000tpic and no tpic faster but for now (now being the very beginning of the hiring cycle (hey Yip, there is that word cycle again, not "boom") your going to compete with guys who have several years RJ pic or military and a rec.
Good Luck whatever you decide. And as you probably already know, it's a big crap shoot anyway. Hope your feeling lucky and give us a call when your 65 to tell us how it all worked out.
Personally I have 27 more years before I can let you know how my "dice rolls" play out.