What I've doing lately has been long exposures if the docks, river and lake at night. I have been amassing a lot of information about low light and night photography, you may try this approach as you get ready for low light or night photos. In the past I have been using flashlight to trace the outline of a subject, as well as firing strobes while the subject was changing position. The possibilities are endless, I hope this helps, sorry I don't have examples to show they were all on film and I don't have them on the computer.
Use a CP filter and see if you can get an assistant to hold a diffusion screen to block out the harsh light coming from the direction that is putting a hot spot on the art work.
If you're shooting mid day surly you can expect wash out in some colours, I recommend taking the photo 2 to 3 hours before sun set, this will increase the exposure but that's not a problem since you have been given permission to bring a tripod. Insure that there are no shadows falling on parts of the stained glass window. The object here is to get even illumination with a light source that will render the most pleasing colour.
I have been working with stained glass for about 3 decades and even longer as a photographer (ammeter). This is quite a simple photo shoot and if you're lucky to get an overcast day you smooth sailing.
Hello all you Ugly Hedgehog, been following but never got my feet wet till now. :)