Aperture 3.6, El Capitan 10.11.5. (I meant to imply that, except for Reinstall Aperture, I had followed all the directions on Get help with Aperture 3 - Apple Support, including "Update to the latest software versions" and "Update to the latest version of Aperture," but I should have specified this anyway.
I have Aperture libraries on external drives, but the three libraries described in my post (35,848 photos, 292 photos, zero photos) are all on the system drive, which is a 500 GB SSD - so normally very fast.
I hope I'm not syncing with iCloud: nothing in the iCloud preferences is checked. Prompted by your question, I just checked iCloud preferences, and Photos is not checked.
Finder says my system drive has 62.89 GB available.
Aperture's Activity window does not show any activity by the time I can open it - when Aperture has finished opening, after about 80 seconds. Is there a way to make launch Aperture with the Activity Window open? A few days ago, I noticed that it seemed to want to do Faces for a while after it opened, so I turned that off in Preferences.
As to Console, it shows lots of messages. I don't know for sure how to identify an error message, but I found no occurrence of the word "error". As it happens, a Time Machine backup was just cleaning up, so I launched Aperture as soon as Console said, "6/25/16 11:38:51.346 PM com.apple.backupd[15747]: Backup completed successfully." I then copied the few dozen lines immediately following that, until it got completely repetitious. The first few lines were:
6/25/16 11:38:58.161 PM com.apple.xpc.launchd[1]: (com.apple.PhotoApps.AVCHDConverter) Unknown key for dictionary: EnvironmentVarialbles
6/25/16 11:38:59.727 PM Aperture[15811]: ProThemeStore: No theme registered with id=1764
6/25/16 11:38:59.727 PM Aperture[15811]: ProThemeStore: No theme registered with id=1764
6/25/16 11:38:59.727 PM Aperture[15811]: ProThemeStore: No theme registered with id=1764
6/25/16 11:38:59.727 PM Aperture[15811]: ProThemeStore: No theme registered with id=1764
6/25/16 11:38:59.727 PM Aperture[15811]: ProThemeStore: No theme registered with id=1764
6/25/16 11:38:59.727 PM Aperture[15811]: Warning: -[NSProThemeFacet imageForState:value:variant:] unable to find theme store.
6/25/16 11:38:59.727 PM Aperture[15811]: ProThemeStore: No theme registered with id=1764
6/25/16 11:38:59.727 PM Aperture[15811]: ProThemeStore: No theme registered with id=1764
6/25/16 11:38:59.727 PM Aperture[15811]: Warning: -[NSProThemeFacet imageForState:value:variant:] unable to find theme store.
Then it began repeating:
6/25/16 11:39:00.530 PM xpcproxy[15813]: CFPreferences could not connect to its daemon.
Preferences using the connection 0x0 will be volatile and will not be persisted to disk.
6/25/16 11:39:00.550 PM com.apple.xpc.launchd[1]: (com.apple.photostream-agent[15813]) LaunchServices returned a bundle URL that does not match with the LoginItem's known association.
6/25/16 11:39:00.551 PM com.apple.xpc.launchd[1]: (com.apple.photostream-agent) Service only ran for 0 seconds. Pushing respawn out by 10 seconds.
6/25/16 11:39:01.794 PM WindowServer[217]: send_datagram_available_ping: pid 456 failed to act on a ping it dequeued before timing out.
6/25/16 11:39:10.565 PM xpcproxy[15814]: CFPreferences could not connect to its daemon.
Preferences using the connection 0x0 will be volatile and will not be persisted to disk.
6/25/16 11:39:10.582 PM com.apple.xpc.launchd[1]: (com.apple.photostream-agent[15814]) LaunchServices returned a bundle URL that does not match with the LoginItem's known association.
6/25/16 11:39:10.583 PM com.apple.xpc.launchd[1]: (com.apple.photostream-agent) Service only ran for 0 seconds. Pushing respawn out by 10 seconds.
6/25/16 11:39:13.791 PM WindowServer[217]: send_datagram_available_ping: pid 456 failed to act on a ping it dequeued before timing out.
6/25/16 11:39:20.609 PM xpcproxy[15815]: CFPreferences could not connect to its daemon.
and so on. It's still repeating the same three lines, almost 20 minutes later:
6/26/16 12:06:06.443 AM xpcproxy[16071]: CFPreferences could not connect to its daemon.
Preferences using the connection 0x0 will be volatile and will not be persisted to disk.
6/26/16 12:06:06.462 AM com.apple.xpc.launchd[1]: (com.apple.photostream-agent[16071]) LaunchServices returned a bundle URL that does not match with the LoginItem's known association.
6/26/16 12:06:06.464 AM com.apple.xpc.launchd[1]: (com.apple.photostream-agent) Service only ran for 0 seconds. Pushing respawn out by 10 seconds.
Any ideas?