Yardman, have found that digging over and replanting an established perennial bed can be more involved than putting in a new one with new perennials.
Am sure, however, that here, breaking up/renovating the clay soil and working in weed-free organic material is key in both cases.
I regularly overwinter divisions of perennial plants in our garden soil in half- and one-gallon nursery pots. However, within the time frame you mention, Cindy's tarp suggestion seems practical.
I also strongly agree with both above about digging up all (or at least most - depends on root depth) of the plants, with division as required and then replanting; that is not just working on soil remediation around the herbaceous plants.