I add and take out plants out of my Walstad tank all the time.
The best way to plant new plants:
cut the roots to about 1/2 inch or so, take the plant carefully by the roots or the tip of the stem with a pair of pointed tweezers, and poke deep into the substrate. That way, the hole you make is very small and the gravel will close around it and little or no dirt will escape.
With larger plants and roots, such as amazon swords, you can lay your finger alongside the plant root, poke into the gravel and then slowly withdraw your finger while leaving the plant behind.
When pulling out old plants, I just grab them low down by the stem and pull slowly and bit by bit - that way, the gravel will fall inwards and close around the hole that is left behind and not too much dirt gets out.
I just pulled a whole bucket full of swords and Vals out of my Walstad tank because they were crowding the other plants - the tank didn't even get cloudy. I'm sure its fine to leave the newts in. If you do get any cloudyness, you could put a strong filter in for a day or so, or else just do a water change.