Update to this. Eventually the tape didn't do so well, possibly because I was doing a very thin thing with no brim, so just to get the job done I put some gluestick stuff on top. Worked very well. Too well - the part just wouldn't come off, and when it did it had tape permanently stuck to it. Worse, the remaining tape was now very firmly glued to the bed
Won't try that one again! Didn't think to try plain copier paper but will try and remember next time. This time I concentrated on applying the tape in a more appropriate way to make it easier to take off without removing the build plate.