Tiling over already tiled floor with underfloor heating

Yes your right it would be a nightmare. I would firstly check original tiles are solid.then use an app primer,latex the floor then re tile on top of latex.you would have to survey your floor heights as this would increase by around 10 to 20mm depending on your new tile thickness

Yes you can layover the original tiled floor without the extra matting, however, the height of your surface will increase, meaning at the door into your kitchen will now be alot higher, so won't be a good finish to the next room. The other thing to note would be that your underfloor heating won't work very well temp' wise, as you've raised the thickness. I completely understand your situation. To note, laying on top of other tiles on a high footfall area, your risking tiles cracking. Bottom line, the old tiled floor + the heating cables would need to be replaced with new. Not what you want to hear I guess, however, you 'maybe' able to save the matting underneath the heating cables. Bear in mind, if tiles do start to crack, then replacing can get expensive to do. So at the of the day, its wiser to rip up the old, and replace all with new. Good luck with your decision.