Are these settings still in place?
Yes, the wireless settings you suggested and all other settings have remained the same.
"The router didn't reboot itself initially after changing the wireless settings (I mentioned the reboot would be random\delayed), so I initiated the reboot through the admin interface Diagnostics tab of the Troubleshooting page(Doesn't count as last reboot I mentioned). Then I poked around randomly through various tabs of various pages/widgets in the admin interface. After about 7 minutes it rebooted itself (This is the reboot I mention)."
Maybe an incorrect assumption on my part but I would assume if there were a config change that caused a random or delayed reboot, a manually triggered reboot would reset both the hardware and software such that anything in the router that would trigger this random or delayed reboot would no longer be an issue. Since the router is essentially just a small Linux-based computer, it should reboot in much the same way selecting the Restart option in Windows reboots a PC causing the hardware to reinitialize and reload the OS.
You didn't make any changes over the 20min? Some configuration changes trigger a reboot by design like other router model
Nope, no changes on any of the pages. Just switching between various tabs of the various pages.
Did your Uptime reset for these?
Yes, the UpTime reset for each apparent reboot.
After the last reboot I closed out all of the open widget boxes on the main admin homepage, except the first two that can't be disabled (Network Status and Linksys Home Networking). I haven't been hitting the admin pages like I was before, I'm just occasionally refreshing the page to keep it from logging me out and the UpTime is back over 3 hours again. I'm not certain disabling the widgets like this will keep the widget code from running in the background or if it will just run when the related page is called. I also just thought to use the Developer Tools in Google Chrome to check the page source code and view the network activity and I can see the router admin page is regularly making four distinct requests to the router and linksys.com. I'll have to check this activity to compare it with and without the widgets enabled and see if I can record the activity leading up a reboot, but that will have to wait until tomorrow.