We have seen the timing be different between TC and TE, so that doesn't surprise me.
How does AWTAccessibleName change? If it's a similar name every time, something like myname1 and myname2, then you could use a wild card in the name mapping so that myname* is always recognized.
We have some cases where the field in question actually changes from being a text box to a combo box after some things load in the background so we had to check for both when we were trying to write in the field. That could be showing up with a timing change.
One other thing we just found was that there was an invisible-to-the-user object loading at the same level as a button so we ended up having to check for the object before we could click the button. That's something else that's affected by timing.
