Good to find confirmation of my guess on this noise! My '03 was doing that screech that I thought was a dry bearing in the starter solenoid. Sort of glad to see it's "only" the gear shaft, and not internal to the starter.
They must have started putting the rubber seals on the '04s, 'cause mine didn't have them, either. The gear and shaft were dry and had no sign of any previous factory lube.
Anyway, things I did different: I pulled the battery AND the plastic and metal battery trays out. Easy to do, hardest was to find the fourth bolt, holding the driver-rear-side of the tray in. Using a panel puller, to remove the clip holding the wire harness to the rear of the tray, made the bolt accessible. Another clip holds the harness to the inner fender; reach into the wheel well to squeeze and release it. Couple more easy-to-get-to harness clips finished the tray removal.
Removed the connections to the starter--the nut holding the main starter cable and the spade terminal-type connector, both under rubber caps, on the solenoid. Took off the two large plastic clips on the radiator hoses and pulled the trans dipstick. Oh, I also took off the O2 sensor(?) connector, by the main starter cable, to get it out of the way, since it was easy. That was all it took.
Reinstall was everything in reverse. Works great, hope it lasts a long time. And it gave me a chance to clean up my battery terminals! Thanks for the .pdf postings, nice to have the diagrams. They did show the mounting bolts as 10mm, but someone posted earlier (and correctly) that they are 14mm.
Cost: ~$12, for some spray cleaner and fresh grease.
2003 Touring/Navi, SS/Quartz, Color-matched roof deflector, wood trim AND shift knob, cargo cover, floor/cargo mats, non-working hood struts, brake clunk, Photon torpedos, and a partridge in a pear tree...
2003 Z06 Vette, MY/Blk, with stuff...
2005 Vibe, beater, commuter, and all around thrasher.
2007 FJ Cruiser, rubber floor mats and bungee cords... ...lots of 'em.