Is there any room between the ends of the two shafts inside the transmission? If there is, I'm thinking I could hammer the CV in and try and break the rust, mud, and whatever else loose which might make it easier coming out.

Is that possible to do without messing anything up?

 

There's a little space between the shaft ends in the rear end and using an impact would probably help loosen the rust also(can't hurt to try) Then you could try again on the jerking the drive shaft out,using a slide hammer,etc. Once you get it out be sure to use anti seize on the splines of the new shaft. OPT

 

I always start about a week before I plan on any work and start spraying down the axles, sometimes it has taken me 3-4 nights of pulling and yanking before they'll finally give and come out. When you get aggravated, quit and go inside, come back out later and yank on em, they'll eventually come out. If you can get some kind of slide hammer affect going it usually works best, be careful with that housing.