Does anyone know what the default shutter speed for the XHA1 is when filiming in the "A" mode under controlled studio lighting?

With 'A' mode it could be anything, depending on the lighting. Best to shoot 'M' if you can.
What frame rate were you using?

Simon I was shooting at 30 frames

A trick I learned from Chris Hurd in my XL1s days...pressing Exp Lock displayed the current settings and kept them from changing. Another press released it back to auto. I'm not sure if this trick works on the A1 in A mode but I seem to recall it worked in the Av and Tv semi-auto modes. YMMV.