Iain, I have been using a related technique for both wood routing and CNC milling recently. Clean the syrfaces, carefully apply a layer of the high quality blue Scotch masking tape to each, making sure there are no overlaps or gaps. Smooth down the tape and get rid of any air bubbles. Then apply dots of superglue to one surface and carefully apply the other on top of it, pressing together until they bond. Once the job is done, with a bit of care you can lever off the cut part with a knife blade inserted between one surface and the tape.
Now for another suggestion. When I did this recently after I applied the glue I put down the workpiece the wrong way up, so it was glued firmly to the tape! I prised it off but the "top" was covered with hardened glue and torn tape. I stuck it down properly the other way up to do the job but was then faced with removing the mess. So I dropped in into a stainless steel pan, just covered with water, and boiled for a couple of minutes. The glue just slid off leaving a clean surface behind.
This suggests that 100 C should be plenty hot enough.
Edited By John Haine on 26/01/2020 20:21:17