A BGA on a mini has one thing going for it: you only need to connect to 1/3 of the pins on the MCU.
This solves the problem of getting the signals away from the BGA.
Also, with with so many pins to choose from, you can make the ones you do use, less contentious.
Even so, it will be hard to get a BGA on a DIY board.
I know you guys are into making DIY boards and I will be too, on my next board but, I have a coupon (if you will) to get some boards made cheap. I get two trys (2 batches of boards).
I going to use it to make a Mini with a full boat STM32F4, 100BaseTX, and any thing else I can cram on there. I think I can do it by putting a BGA on a 4 layer board with plated through holes.
If you make all the balls sit on plated through holes (or at least the ones you need to connect to) shouldn't you be able to reflow a ball from the back side?
I'm back to trying to fit some RAM on there too.