When my son was tested as a kindergartner, the school psychologist broke the testing into parts, over a few days. But she was young, very friendly and engaging, and had met my kiddo before. She also said he took awhile to open up to her. She tested him more for achievement on WJ-III, if I recall, since we already had private IQ results. I think they also observed DS and filled out some social/emotional form.
It sounds like your school psychologist is doing a good job making sure that he is getting decent answers, instead of just marking off that your DD doesn't know the answers. Most school pychologists are more familiar with testing for LDs, and it sounds like this tester has only tested older kids for GT.
If they give you any indication that the results might not be very accurate because your DD has been so upset, my only other thought is maybe you can ask if there is another school psychologist that your DD might be more comfortable with. But from your description, that person would probably take time for your DD to warm up to as well.
