I took all the steps you wrote down for me and I got JOdin working, finally..
But there goes something wrong still.
Because ... uploading the stock ROM (1,5GB) should take a while, is not done in just a few minutes.
Uploading all the files should take at least 10 minutes to complete.
Yet, in the end, it does say reset in green though.
And I'm quite sure that something is wrong, because I didn't see the blue status bar on the Samsung tablet during the upload process.
Uploading the extracted files seperately in Heimdall, 10 pieces out of the stock ROM, will take 10 - 15 minutes to complete and the largest of them all is the 'system.img' file which is 1,2 or 1,5GB in size.
With Heimdall I do see the status bar in both the program while uploading and in blue the same status bar on the Samsung tablet.
On the end of the day, I still have a rooted and faulty Android system running on that Samsung tablet.
Somehow the clean factory default is not loaded when the Samsung device reboot after all uploads with Heimdall.
Although the software uploaded is Android 4.4.2 for Tab3 7.0 8GB WiFi, with all the correct changes, date of build and country code.
Is there a final method to clean out the current faulty content of the Samsung Tab3 device?
Edit: ok I just found out that fastboot does not work with samsung devices
Try to use odin on windows https://samsungodin.com/ or through wine on linux but I highly doubt that this would work.
I am sorry, but at this point I can't help you more. I haven't used a Samsung device in about 4 years and have no idea any more about all the problems and kinks with odin or generall samsung devices.
I wish you the best of luck.