Thanks all for the suggestions and help! The luthier idea did scare me a little : )
Yesterday I got out and bought some fine steel wool (they did not stock #0000 so I went with #000, which is no problem) and removed all the old Aquila's. I mask-taped everything and had a go. I think the workers at the Kala factory used a rough file on some frets because some tiny grooves were visible. After the first round of steel wool I used some 1200 grit sandpaper and sanded a bit (equally). Then I finished with some steelwool and the frets ended up shining like never before!
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Restrung it with some new Aquila's I had laying around and the bending problem seems to be solved! While opening the new pack of strings I read about how the nylguts are 'liable to suffer from cutting edges'. I guess it was a combination: the rough frets damaged them and the damaged strings 'contributed' to the problem/sound as well.
I am a happy uker again! In the near future I will be trying some D'Addario J71's... I am just too curious! Anyone using these on their (Kala) tenor?