2nd-3rd Shift 'flare'
Hi lebar, actually your trans is probably just fine. Our automatic trans actually does several things when shifting from 2nd to 3rd. It has to release the second gear band, next [ believe it or not] shift into FIRST gear, then into third. [I'm pretty sure I have described this right. ]
If I remember my 'lesson' with Bill K, third gear has first and third clutches engaged at the same time. First gear clutches have to engage first, then the third gear clutches.
What you are getting is a slight 'flare' of rpm between the engagement of these clutches.
I may have this a bit wrong, if you want the straight scoop, call Bill K, or go their forums and read up on it,
www.dieseltrans.com 1-866-504-4002
The slight flare that you are experiencing is actually desired, because this means that you are getting the correct sequence of events inside your trans. If not what can happen is a 'bind shift' where the clutches are engaged at the same time, [not in sequence], and the trans is for a moment binding internally, this creates very high wear and temperatures.
My DTT trans has this slight RPM 'flare' on the 2-3 shift under light throttle, but it is not there with lots of throttle. This is perfect according to Bill K.
When you get the 'hesitation' in reverse, is this the first motion you are requesting from the trans ? Say like backing out of the garage or parking space first thing in the morning? If so you are probably experiencing a bit of 'drainback' there is a check valve that leaks a bit, and allows some fluid to drainback into the pan overnight. If this describes your situation, just shift into neutral for a moment [before selecting reverse], this will circulate the trans fluid quickly, and you should not notice the hesitation as much if any.
I hope this helps. Greg L The Noise Nazi