I'm totally editing this because I didn't read the link provided and I think it would work SO well! Ignore my post below.. I was trying to do it the hard way all those times. See.. even a big know-it-all like me can still learn something great here!
I'm an experienced diaper seamstress, and for the life of me, repairing elastic in a serged diaper is my worst nightmare. 9 times out of 10, I can't serge it exactly right and I get funny serging around the snaps or I end up serging too close to the elastic etc.. It's just harder than you'd think. do try it..if you aren't going to use them the way they are anway, you have nothign to lose. But, be prepared and don't get too frustrated wtih it. If it seems like it's not going to work, let it go to diaper heaven and move on. I've spent HOURS trying to repair serged diaper elastic and in the end wasnt' happy with the results. I think some people are more talented in that department and maybe I'm just not one of them (I need lots of room for error and since it's already been serged and trimmed, that room for error is all but elimiated). If it was me.. I'd take out the old elastic and use what's left to make a pattern from the diaper instead
and salvage the soaker if it could be salvaged.
If you REALLY don't care how it looks but just need it to function again, you might consider just sewing new elastic onto the outside of the diaper directly over the old elastic Just tack down, pull the elastic taunt as you sew down the elastic and backsttich at the other end. It'll be exposed, but won't be on baby's skin and will make the diapers function for awhile longer.
Hope I don't sound too jaded.. it's just never been a fun project for me.