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It would be best to catch them right after they flower, and dig portions of the plant up. This plant will take off and grow like wildfire no matter when you transplant, as long as they aren't dead. Here is an article on the plants: https://www.gardeningknowhow.com/ornamental/groundcover/snow-on-the-mountain/snow-on-the-mountain-plant.htm

There is nothing that can be done. Variegation is a genetic mishap that only shows in clusters of cells at the originating growth point. Anything that does not grow from this original cluster will not have variegation.

Unfortunately, there is no way to control this, and it may turn up again randomly in the future.

This can be due to lack of sunlight. This article will help you.

https://www.gardeningknowhow.com/ornamental/groundcover/snow-on-the-mountain/bishops-weed-reversion.htm

Snow on the mountain, Cerastium tomentosa doesn't like heat. If you water regularly, you may be able to keep it from browning. Another solution is to put it in afternoon shade. Like my lawn, snow-on-the-mountain will green up again when cooler weather returns.

Snow on the mountain, Euphorbia marginata, is one of those plants that was highly touted as a groundcover at one time. Now, most gardeners find it a curse especially when it is in a bed with other plants. In general, plants expend a lot of energy getting through the winter. Putting out the spring's first leaves nearly depletes stored energy. This is the optimal time to start a weekly cutting/weed-whacking program. It may take more than one year to eradicate it but regrowth will slowly decrease during this time. Combine this with sheets of heavy cardboard to deny sunlight, and resulting photosynthesis, where this is practical. Good luck!