I purchased a new pilot bearing for the flywheel to see if replacing it would help with the rattles.
Flywheel - it's what's for dinner! I've found during my transmission rebuild that heating up components in the oven (200 F) sometimes helps with removing the bearings, so I heated up the flywheel prior to replacing the pilot bearing. I also put the new pilot bearing in the freezer to make it smaller.
Here's the heated flywheel, clutch side up. I put a 9/16" socket on the pilot bearing and placed a steel block over that to even out the pushing forces. After a few good whacks, the bearing popped out.
Here's the re-installation. Again, I put the new bearing in the freezer to help it go into the hot flywheel easier. I first tried to line the new bearing up and used the steel block to keep it straight while I tapped it in. I used the 9/16" socket again to finish the job.
I searched online to see which way the bearing went in. The one comment I found online said that it didn't matter; however, if I look at the bearing, one side is clearly wider to present the needle rollers to the incoming shaft. I chose to install the bearing with the embossed text on the rear (non-clutch) side to see if that would help.