I often referred to my '04 2500 HD 2WD as the 'One Wheeled Wonder'. It came from the factory with an open differential and I can honestly say I feel the OP's pain. I have been stuck on boat ramps, wet grass, and snow/ice were a real treat.
In 2009 I finally found a fantastic deal on an Eaton Posi LSD unit. I thoroughly researched the merits of limited slip and locking differentials and finally decided I wanted the greater 'road worthiness' of the LSD as opposed to the locking diff.
I've been very happy with my decision and can say the Eaton Posi got me through many situations that would have previously left me spinning one wheel in a helpless truck. That's not to say I haven't been stuck even with the posi. But, when I have been stuck I still got out with a tow.
I have made the truck work and I won't be trading just to get a 4X4. The truck is paid off and with low miles, so I'll be using it for a long time unless something drastic happens. But, I do believe my next truck will be 4X4 just so I have greater confidence in getting out of poor driving conditions.
As a side note, I've done a little searching and I think I could possibly retrofit my truck with a manual transfer case, and front differential from a wrecked truck. As best I can tell, the 2WD 2500HD's are totally identical to the 4X4 trucks minus the extra driveline components. Unfortunately I don't have an abundance of time and it's really not important enough for me to search high and low until I find all the components. So, I guess it will just have to remain a pipe dream.
KJ