I remember when I was a scout, playing british bulldogs (don't know if you yanks heard of it). Basically it was a game where you ran across the hall and people in the middle had to either lift you off the ground or get you down and pin your shoulders down (no rules except no striking).
Anyway, I hadn't done any aikido, but this big scout ran towards me with his head down to push me over; I moved out of the way and pushed his neck down (like the start of an irimi nage) and he went flying.
Didn't know that about 5 years later I'd start aikido and find it difficult to do the exact same thing!
I think randori every night is perfect - in fact I might try that one in my class. It developed awareness, body movement, timing and miai - the basics of aikido which are often forgotten when you spend the time just learning new techniques.