Those Radiola III xfmrs that are sold by AES and RadioDaze will physically fit in the original Radiola III and IIIA cases. I don't know if they will fit in yours. Hopefully somebody here will know. Otherwise, you can post a photo and measurements of the xfmr, and I can verify if the Radiola III xfmrs will fit, physically.
Your Radiola Grand is a very valuable radio, so you want to try to maintain its original appearance.