I feel that I should follow up this post with one that tells how it actually turned out:
I did not get a convenient parking space. BUT . . . I did get my favourite dressing room and some not-too-faded gowns and a warm blanket without asking. I also got a little computer-printed "diploma" to certify that I had completed my prescribed radiation treatment, with the names of all the technicians on it, and tied with a little blue bow. That was better than a bouquet of hazardous toiletries, by a long shot. Also--takes up less space.