I found a video of Yamada Sensei showing 4th kyu techniques. At [2:50] he shows two tsuki irimi nage. The second one looks close to the one I think Anne Marie was describing, which is nice. I noticed that Yamada Sensei does not grab the tsuki wrist at all. http://www.youtube.com/watch?v=--S-w3L-rRs
Anne Marie: Thank you for the video post - that nagae's third tsuki irimi looks like how you described, and with no wrist grab... kind of along the lines of how Yamada Sensei shows it. I like it.
I'm starting to think that for this version it is better to do tenshin and cut/parry at the elbow and to not capture the wrist as the initial movement. This is neat to get advice from all of you.