Wont replanting mess yup the root system?
Nope.
Crypts might melt, but not to worry. They'll re-adjust. Leave a small portion of the roots. Trim the long stuff.
For other rosette plants (smaller swords, sag subulata, etc.), trim the roots back. That way you won't have bits sticking out.
For stem plants, pull the plant, cut stem into thirds (depending on length). Trim roots off bottom and replant. Plant the middle thirds and tops. Soon you'll have a nice bushy mass. It's more time consuming, but you'll have better success if you plant the stems individually rather than as a bunch.
For any plant tied to something else, just trim off roots that are growing anywhere you don't want them. Plunk object back in tank where you want it.
Finally, buy yourself a long, thin pair of tweezers. Much better than using your fingers.
Blaise