I've been lifting and cleaning and clearing and refereeing my garden all this year following a forced, post-op absence of almost 2 years. In that time, along with several nasty, pernicious weeds, my garden has been overun by a pink geranium that has spread and seeded itself about with gay abandon. I've been digging them up since early spring and have potted some on to give to people who I know like pink or need some fast ground cover but there are limits and huge amounts have gone in the compost bins.
Whilst clearing the borders, clumps of any plant I want to jeep get bunged in buckets and troughs and any container I can find and can stay there for weeks sometimes while I dig over and clear the beds and then clean their roots. I've had very few losses doing that.
Where I haven't yet got other plants to replace the geraniums I've simply cut them back hard once the flowering is starting to fade and then they at least grow back healthy, fresh looking foliage so look better. I will even get a second set of flowers to keep things looking good till the new babies get big enough to plant out in their place.
Japanese anemones aren't a problem here but I do find phlomis russelliana a bit too happy and either pot up for swaps or bung on the compost heap. As long as you can keep things you do dig up sheltered from strong sun and adequately moist I find them very forgiving when needs must but the best time for lifting and dividing most plants is still spring and autumn.