You need to get a rear-end spreader or you'll never get it out. You literally stretch the case just a little then you can pry it out.
The Axle Housing Spreader (J-24385-01) will run you $300 to $400 but maybe your local rental yard has one. Setting up backlash and pinion depth is critical and can be kind of tricky. For good info:
Randy's Ring and Pinion
http://www.ringpinion.com/
and
Richmond Gear
http://www.richmondgear.com/01instructions.html
Have you considered getting a complete used rear-end from a reputable salvage yard? Check out Car-Parts.com.
The same rear end was used in Escalades, Suburbans, Yukons, and Chevy/GM trucks so there is a buttload of rear-ends (pun intended) with low miles out there.
I just did a search for a "rear axle assembly" for your vehicle on Car-Parts.com using my area code.
http://goo.gl/AdNu8
I recently replaced the rear-end on a 1998 Ford Ranger. I found a used one at a local salvage yard via Car-Parts.com that had 76,000 miles and was in "A" condition. It took about an hour and a half to bolt it in, install the cover, connect and bleed the brakes and add some GL5 oil. Oh yeah..the rear brake shoes and drums looked nearly new.. like the guy just had the brakes done before he wrecked it so I got a free brake job too.