I took apart the front end and examined the axle, bearings, seals, etc. The axle was scored at one bearing, with dark looking grease that looked and smelt burned. The spacers were missing most of the coating.
I'm going to go ahead and replace the bearings, seals, and spacers. I didn't have the parts on hand, so I put high-temp grease on the axle and seals and put it all back together until I can order what I need. Lo and behold, the squeaking is gone. I also noticed that the axle nut had been tightened WAY too tight.
Thanks for the suggestions!