No Dig for perennials
I guess the biggest change in a perennial bed, from what you have been doing, to a more no dig approach, is to continue to add manure, compost or other organic material, but to simply add it as a mulch layer, avoiding bare soil if possible, and not needing to dig anything in.
I significantly expanded a mixed border with this method. The issue is that where you lay the cardboard and add a thick layer of mulch you raise the soil level which would leave the existing plants (in your case) in little wells. I extended my border outwards, covering lawn, so the "join" is kind of buried in what is now the middle of the border. The ground is not as flat as a pancake so over the past 18 months the two parts have married together.
I guess what I'm saying is it is a method that works well for veg, mixed border creation, perennials, etc. Char;es Dowding's book does have a small section on creating flower beds rather than veg ones. The section that was created by no-dig in my garden is significantly less weedy and what does emerge is pulled out by hand. Some borders are 3-4m deep and I'm adding stepping stones for access. I will lift and divide perennials (in particular, my asters and Siberian irises need regular division) and replant. I make sure not to disturb or turn over the soil inbetween plants. All new areas I am creating in the garden are no-dig.
If you embrace the no-dig method you'll never look back.
I went on a garden tour of the new planting at Chatsworth, with the head gardener and Tom Stuart Smith. To get the huge areas of planting established on very difficult shale subsoil, they simply laid 200mm depth of green waste, let it bed in and sprayed off any weeds that came through, and planted directly into it.
! Good video suggestion...