From my personal experience, almost none of my free score reports panned out. Between taking the general and psych GRE and to actually applying, my knowledge, specific goals, and especially school choices changed dramatically. Most schools that I thought were my top choices didn't even make it to the application. Maybe this is just my own experience and is unlike others, but a year before apps, I made my choices primarily based on school reputation. Then the summer before apps, I started to look into the actual prof's bios, papers, interests, future directions and other aspects of the programs like match rate, acceptance rate, etc and I narrowed it from 20 schools to 10 and ended up applying to 7. Of those 7 schools, I believe 1 was my original "top choice" but by the time I sent in my apps, I realized their match for me wasn't great.
So in other words, I wouldn't worry too much about it. Similar to above individual, I would take advantage of the free scores if you think you did relatively well. While you can't predict if you got a 95th or 96th percentile, I'm sure you know whether you were in the 50th or 80th percentile. I'm not sure if this is the case, but I believe that when I sent my general scores, my psych scores went with it with no extra charge? I don't know though, you need to check (the whole app process was a blur).
I think what happens is if you send your scores that early, they just have it in a database and then match your name when you send in your applications. Just make sure your first, middle, and last name that appear on the test is exactly as it is on your app.
Also, the whole app process wasn't actually THAT expensive for me. I thought I'd spend at least 5K, but ended up spending significantly less than that. However, that may be a product of applying to "only" 7 schools.