Wrap a ratchet strap around the sway bar and lower control arm and tighten down. This should compress the bushings enough to screw on the nut.

 

Thanks for all the great suggestions! At the same time I was wrestling with the sway bar linkage, I was also dealing with what I thought was a failed caliper. I replaced the caliper, but the horrible grinding noise continued. So, due to timing, I took the Suburban to the shop because I was leaving the next day on vacation, and needed to get this thing road-worthy. The noise wasn't coming from the brake, but instead from the hub bearing. So, when they replaced that, they also replaced the sway bar linkage. I'm sure one of your suggestions would have worked, I just wish I had enough time to try them out. Thanks again for all the good advice along the way!