I loaded up the new Teensyduino 1.17, but I don't see 3.1 listed as a board, is this correct?
When you run Arduino and click Tools > Boards, you should see this:
(click for full size)
If Teensy 3.1 does not appear (as shown in this screenshot), then you simply have not correctly installed Teensyduino 1.17.
You don't need to uninstall anything before upgrading to the new version of Teensyduino, correct?
Usually the Teensyduino installer can install into a copy of Arduino that already has an older version of Teensyduino. If it can't (because some file within that copy of Arduino has changed in any way the installer can't recognize), the "Next" button will not enable. When the installer can't work, you will know, because you will not be able to complete the installation. In those cases, you'll need a fresh copy of Arduino 1.0.5.
However,
you MUST select the copy of Arduino you're using (which is almost certainly where things have gone wrong). Here's another screenshot.
I installed the 1.17(final) version in the same directory that I had 1.17 (rc3) in. That is the correct procedure, right?
Obviously something wasn't correct, since you're not seeing Teensy 3.1 in the Tools > Boards menu!
When you say "installed ... in the same directory", what precisely does that mean? If you simply put the Teensyduino.exe in some folder on your hard drive, then no. You must run the installer, and when you get to the step shown in the screenshot above, you must select the location of Arduino.
If you have more than one copy of Arduino on your computer, you must select the one you're actually using. For example, if you have a copy in C:\arduino-1.0.5 and also a copy in your "Downloads" folder, and you select the one in C:\arduino-1.0.5 while running the installer, but then double click the one in Downloads, then of course you won't see any results, because that other copy wasn't changed by the installer. It only writes Teensy support into the copy of Arduino you select.
This problem is unfortunately pretty common on Windows, partly because the modern trend in Windows is to show these virtual locations in many modern Windows programs. It's pretty easy to unknowingly have more than 1 copy of Arduino on your hard drive, because Windows doesn't always make it clear where you're actually running program from and where files are actually installed.
If you're totally stuck, I'd recommend you simply download a fresh copy of the Arduino 1.0.5 zip file (not the installer) from
www.arduino.cc and extract it to a known location on your computer. The key point is to remember where you on your computer, the precise folder location, where you extracted the zip file. Before extracting, make sure you do NOT have a prior copy, so you're certain this is a freshly extracted copy. Then run the installer, and carefully select that location. After installation, run Arduino, again being careful to navigate to that location. Simply clicking any existing shortcuts might actually run another previously installed copy of Arduino, so please be careful to use the copy which is definitely in the same location that you selected while running the Teensyduino installer.