I did this same job on my 2001 Blazer. I don't recall the springs being an issue and the bushings can be tapped into place with a small hammer. (Go easy on them) The real issue is, the way the pins go in you have to hang/support the door so there's no weight on the hinges during the pin removal.
Although it sounds primitive, I used a come-along attached to the roof joists in my garage, rolled down the window, wrapped a towel around the top of the window frame and put the cable to where it was balanced well enough to do the work.
It's a bit of a pain, but once you get the door suspended the rest isn't really difficult or time consuming.
One last thing, I wash my Blazer quite a bit and I think this had a bad effect on the wear of the bushings. On the way back together I smeared anti-seize on the bushings and pins to help avoid water penetration. It still seems to be helping 60,000 miles later.