Looking at the service records, I see non HONDA ATF was used. If I cycle new HONDA ATF (500 miles on one change, than perform the following change) would the trans shift smoother?

 

its highly possible. Honda transmissions do not take well to non honda ATF well at all. And when you put the new fluid in, you need to drain the old stuff, fill new stuff, and let it run for a minute or two. Then repeat two or three times. This is to try and get all the fluid of the torque converter and any left in valve body and clutch packs that was not drained from the first drain. This should get most of it out. Then changing again down the road in a few hundred miles should do well.