Okay I think I have narrowed down what could be causing this.
First, did you update officially or by flashing a ROM through recovery?
-to my understanding if you updated officially then the new bootloader will cause some bugs in older versions of recovery, that may have caused the .zip to not flash correctly.
-I do believe that a newer version of CWM is available on XDA forums that is compatible, I would post a link here but I can't.
-Another fix may be to flash stock recovery, but i think nole Kat may have a kernel that needs to go with it. (not 100% sure)
Second, when you flashed the custom ROM did you do a full system restore before hand?
-a dirty flash between these two versions could be affecting the file system as KK changes the directory of the internal SD Card.
-this should be done from recovery menu, I would also wipe the cache and dalvik cache, you can try this then reboot normally to see if it fixes the problem, if it doesn't try installing a different 4.4.2 ROM (I use StockRom 1.7), just make sure to wipe everything again.
Now to answer your question, I do believe its possible to downgrade from 4.4.2 on the tab 3, but it would be a rather tedious task, I know it can be done on others, however I don't know the exact method to doing so, either Google or the XDA forum would be your best bet to find it.
Also, if you still have root problems there is a new method by using odin to flash the new CWM then flashing a .zip file, this can be found on XDA
My device>>sm-t210r - rooted - PhilzTouch (6.23.9) - (CustomRom) StockRom KK Version 1.7 (unofficial t211 KK port- works great)