Hi Monica, I realize this is late but since you have had no answer, maybe I can help a little.

I think either option is doable, and maybe you have already lifted them, not getting any advice here. But I think I would lift them at the same time that I added new soil. Mainly because it limits disturbance to one event rather than two. Plus the new soil will have new nutrients in it and will help the perennials settle back in.

Fall is a dicey time of year, depending on temperature spikes and rainfall (or lack of it). If you catch the plants while they are still in their winter dormancy, and if you dig down deep and get all the roots or at least as much as possible, it is possible to move a plant in the spring without it "being aware" that it has been moved. It will wake up in its new spot and proceed as usual.

Just my two cents. --Ilene