[Galaxy Tab 10.1 Q&A, Help & Troubleshooting] tpsped:
Success... at last!

I did download the correct stock ROM (including boot.img, recovery.img and system.img). It was found as XAR-T580UEU1APG1-20160905144918.zip located HERE. This is the correct stock ROM for this device.

Before trying any of these steps, make sure you have installed the latest Samsung drivers. It may take a few minutes during some of these steps for the drivers to install. If at any point during these steps Windows has a notification that it is installing drivers, stop and wait until the drivers are finished installing. I noticed that a "Gadget Serial" installed when I connected my tablet to Odin in Download Mode. If that happens it's fine, let the drivers install before moving forward. Also it should be noted that this was performed using a PC with Windows 7 Professional.

COME WITH ME ON MY JOURNEY TO FREEDOM!

1. Boot in stock recovery

Hold Volume Up button + Home button + Power button

-OR-

Power off, wait for battery charge screen to come up, the hold Volume Up button + Home button + Power button

2. Wipe data & Factory reset

Press the Volume Down button until wipe data/factory reset is selected (highlighted/colored), then press the Power button, on the following screen use the Volume Up button or Volume Down button to select Yes and then press the Power button, once your screen is back on the main screen where you started, continue to step 3

3. Boot to Download Mode from stock recovery (do not boot to Android OS)

Press and hold Volume Down button + Home button + Power button

4. Odin, prep for flash and connect tablet (latest version, v3.12 at the time of this posting)

Open Odin and click options, then uncheck Auto reboot, and finally plugin your the USB cable into your tablet and PC. Once Odin recognizes your tablet, the far left box under ID:COM will turn blue and the Log tab will say "Added!!"

5. Flash TWRP custom recovery (twrp-3.0.2-0-gtaxlwifi.img.tar)

Click the AP button and find where you saved the TWRP zip.

Once the box next to AP is checked, click Start, if successful the Log will say "Successful 1 / Fail 0".

If this was successful, move on to step 6. Note that you don't have to unplug your tablet from the PC, just close Odin.

6. Boot to TWRP recovery (do not boot to Android OS). This step can be a tricky one and requires good timing. It is important to do these steps quickly.

From Download Mode, press and hold the Volume Down button + Home button + Power button (the Download Mode combo) until the screen goes black, then immediately press and hold the Volume Up button + Home button + Power button (the Recovery mode combo). You must switch from the Download Mode button combo to the Recovery Mode button combo before the Galaxy Tab boot screen appears. If you're too slow, you will have to go back to flash the stock ROM back to the tablet and start back at step 1.

Once in Recovery Mode, swipe the bar at the bottom of the screen, tap mount, and verify that the box next to Data is checked. Once that is verified, you can flash the SuperSU (SR4-SuperSU-v2.78-SR4-20161115184928.zip).

If you had not already copied it to your tablet, you can do this now since Windows should recognize it and allow you to copy the zip file to the table. You can also copy it to the external SD card if you have one and flash from there.

Once you have the SuperSU on your tablet, tap install from the main TWRP screen and then find it (you may have to search the folders), tap on it, and then tap install. If you are wanting to flash Xposed (xposed-v87.1-sdk23-arm-custom-build-by-wanam-20161125.zip), or the boot image patcher (no-verity-no-encrypt_ashyx.zip), do not check the reboot box. Just swipe and flash SuperSU. Once done, go back and select the Xposed zip and flash. Once it is finished, go ahead and reboot, unless you also want to flash the boot image patcher to remove encryption. If you do, install, flash, and then reboot system.

NOTE: If you are going to flash all 3 (SuperSU, boot image patcher, and Xposed) do them in that order.

7. Confirm your work

Once Android is booted, check the SuperSu app and you'll verify you're rooted. Go ahead and reboot into TWRP recovery and you're Data partion is mounted and unencrypted. Now go ahead and install Xposed Installer (XposedInstaller_3.1.1.apk) and you're ready to download and use Xposed modules.

I followed these steps and have my Samsung Galaxy Tab A 10.1 (2016) (Model SM-T580NZWAXAR) rooted, unencrypted (data partition mounts in TWRP recovery), and Xposed framework installed flawlessly with no boot loops, no lost Data partition, no Encryption errors, and no hassel. All credit for the mentioned files and part of the steps to achieve this go to those that the credit is due. My contribtion is merely my journey and this 5 times tested, yes, I completely wiped and formatted my entire device and did this method 4 more times after I had success before writing this, to help others that might be frustrated for days as I was.

:victory:FREEDOM!!:victory: