Sounds a little like you have the FF bug,,and looking for someone to confirm going full frame.
Just my opinion,,the 70d would work real nice for your requirements. Your going to lose the reach if you go full frame,
I went from a 50d to 7d, I only use my 7d shoot sports. The 70d is going to be better at high iso than my 7d.
I think the 5dmkiii is a great, great camera, For a amatuer dad I can't justify a $3000 body(5diii)But then again I can't justify the harley sitting in my garage either.