Finally got the handle repaired. And I have a few suggestions and comments for anyone who is planning to do the same.
I had no trouble getting the handle out...removed the interior trim, took away the waterguard, marked the latch rod where it fits into the retainer so I could reinstall it at the same length, unsnapped the latch rod retainer at the latch (the retainer did not break, but having a spare one on hand is still a good idea...they only cost $2.06), rotated the latch rod around and up until I was able to disconnect it from the handle, drilled out the handle rivets, and then pulled the handle assembly out of the door. Next, I had to remove the two rivets that hold the assembly together and here's where things got lousy. The rivets were almost flush with the surface to begin with, and I was only able to remove one of the two with enough metal left on it to reinstall it properly and re-mushroom the end. More on that later. I then did a little rebending on my Tru Value spring and fitted it into place. Note...the handle actually has two springs...one on each side, and they are wrapped in reverse of each other...you will only be able to replace one spring with the Tru Value spring. Even so, it is working fine, for now at least. Anyhow, I put the assembly back together and then reinstalled the rivets. One went in OK and I was able to mushroom its end. However the other one was now so short I finally had to drill a small hole into the end of it, install it, and then affix a small drop of solder to (I hope) hold it in place. What a pain in the ass!!! I ended up messing around with these rivets for several hours, and if that drop of solder isn't really affixed well, I'll get to do it all over again. ***IF*** you can get the rivets out cleanly, this portion of the reassembly shouldn't be a problem.
Anyhow, I finally got the rivet problem more or less solved, refitted the handle to the door, affixed it with 1/4" X 1/2" bolts to replace the drilled out rivets, refitted the latch rod to the handle connector, snapped the latch rod into the latch end retainer, and buttoned the door trim back up.
The whole job would have been over in about one hour if I had been installing a whole new handle assembly. I hate to admit it, but this job took me almost four hours because of the damn rivets. (BTW, these rivets are not easily duplicated with a bolt or some generic rivet. If you tear apart a handle you'll notice the rivet has two different diameters, and if you were to try substituting a long thin bolt, the handle will be sloppy on it. If you have a machine shop to turn a new rivet, that'd be a whole different matter.) Soooo...if you are planning to fix a broken door handle spring, you might want to consider replacing the whole assembly. They cost about $60 and come prepainted.