Wes always ran 3rd locked up. What you hear at the end is the converter unlocking. Sometimes its hard to even tell when the transmissions shift, if you have a fairly loose converter and are in 4LO.
As far as the video of your pull...
It sounds like to me that it jumps right through 3rd gear into over drive. I notice in your signature that your truck is an 05. For some dumb reason the 2005s do not come with the option to lock out overdrive, which of course is what you want to do when pulling. On all other trucks with the exception of the 2005 models, you have both a tow/haul feature and a OD lockout function. It has been my experience with my 47RE that if you just lock the converter manually with a switch, it will quickly shift up through the gears. Before I permanently disabled my overdrive, a couple of times I forgot to turn the overdrive off before I pulled. My transmission would stay in 3rd or "Drive" only for a second before shifting to overdrive, where it would kill out.
My advice is to first figure out a way to disable the OD. There are a couple of options that I know of. Dodge has a TSB out that will allow you to be able to lock out overdrive. Unfortunately, you will lose your tow/haul feature as it will be replaced with OD lockout. Here is a link that explains it in more detail.
TSB 21-006-07 The other option involves purchasing a module from BD Diesel which can be found here
BD Power - Product: LockOut Overdrive Disable
After you are for sure able to lockout overdrive I would suggest that you start your pull out with the selector in "2". Spool up as normal and let it eat. Eventhough the selector is in 2nd, your transmission should start in 1st (unless you have a manual VB). Once the turbo spools the truck should quickly run through first gear and shift to 2nd. About as soon as the transmission hits 2nd gear, flip your switch to lock your converter. Once the RPMs climb to an acceptable level, go ahead and manually shift the selector into "D" (be careful not to go to far and put it in neutral :doh: A ratchet shifter would be a good investment). Your transmission should shift to 3rd with the converter locked. Since you have OD locked out, it should stay in 3rd until you unlock the converter. If you can, let the truck spin out in 3rd with the converter locked. However if its going to pull the RPMs down low enough to snuff the charger, go ahead and unlock the converter and keep the hammer down until you stop moving. This has been a tried and true method for me. Granted I have a 12valve and a 47RE, I think the same process should work well for you also.