I suggest checking the adjustment of the cable to the transmission. It not only controls the downshift – passing gear put it also affects the transmission fluid pressures.
The 4L60 and the 700R4 are same but do not confuse these with the 4L60E which is different.
This site has very detailed information on adjusting the cable to the transmission:
http://www.tvmadeez.com/article/index.php
Here is another part of the same site:
http://www.tvmadeez.com/article/part2.php
Here is another good site:
http://www.transmissioncenter.net/700r4.htm
You should start a new thread for discussing the hesitation because it could get to be a very long discussion.