I have the same uke. I do not have it near me, but IIRC, the action is not that hight on mine at all. I wont be able to measure it and report back on that until maybe tomorrow (FRI) evening.
I dont have a string height gauge to measure it with, and my preferences may not match yours, nor can I guarantee that we are using the same strings, but I will caution you that any 'absolute' measurements you read about are not going to match your exact playing style, nor your actual instrument, when in fact string height, and what you've encountered as playability issues, are all relative to the instrument and the preferences of the player.
However, I have a few thoughts for you...
1. You could call Kala, it does not matter how old your uke is or how long ago you bought it, or even if you bought it used. they have a tech support number on their web site, and since they made the uke, they can tell you how it was supposed to be shipped when it was made. That would be the only valid reference I would consider if you want to use a ruler instead of your own 'feel' for string height... Many folks will tell you about stacks of business cards, or the width of a guitar pick (I admit that I too have been guilty of that in the past), but these are only a reference, and not a mandate.
2. On Kala's web shop (linked from their main page), under accessories/parts they sell 5mm, 6mm, and 7mm saddles for like $3-4 each that will fit the KA-T. I have bought one of each size in order to swap them out if/when I use different gauge strings. Mind you this is the
SADDLE height,
NOT the height of the strings from the top wood of the uke body at the bridge. If you get the different height saddles, you can easily swap them out and still have your 'original' in case you want to go back, and also just in case you still need to make adjustments, you will have various spares to try again, so you are not left without any saddle at all, if you file/sand it down too far.
3. If this is your first attempt at modifying the saddle on a uke or guitar, I HIGHLY recommend watching like at least a dozen youtube videos on the subject and even more than that if needed until you have a comfort level with doing this yourself. YOU CAN DO THIS YOURSELF, easily.
4. If you are still lost or unsure, you can take it to a luthier or guitar tech at a local music shop and have them look at it, but you will probably pay at least $50 for any work done by a competent person, and for a uke that sells new @ retail for $115 everywhere, this seems like a lot to spend to me.
5. I have done much worse 'modifications' in pursuit of better playability, some were complete failures on the first try, but I persisted and educated myself until I got it right, and always figured on having spare parts (the first try almost always gets trashed, due to imprecision, impatience, lack of experience or some combination thereof).
6. If you are handy with a file and/or sandpaper, AND you ONLY modify the saddle (the white plastic/bone/other-material insert) that should be easy to remove from the slot in the bridge once the strings are loose enough, this should be a piece of cake to fix.
However,
GO SLOW. Coarse sandpaper (100 to 400 grit aluminum oxide) can take off like 0.5mm in 2 strokes on a plastic saddle, and that by itself is enough to alter the string height/action enough to feel a difference. You also want to make sure that the sandpaper is on a perfectly FLAT surface otherwise when you sand down the bottom of the saddle, it will be uneven, and in fact create a worse problem. Alternately, you could also file/sand down the top of the saddle, but then you migh have to re-crown it to put a nice beveled edge on it, and now you are also getting involved with the intonation, and you've only got like 1/8" of material to work with, so this requires a bit of finesse and tons of patience (having spart parts beforehand is a lifesaver, see #5 above)...
Hope this helps...let me know if/what you decide and I can try to help further if possible...
Other members here on UU might have alternate ideas, and you might want to consider and integrate them once the others chime in too.
-Booli