What is the best way to transfer your established ...

DWC? you have to stress the s%$# out of it, unless you want a bunch of dirt clogging up your equipment.

maybe some of that garden liner that allows roots to grow through would retain the soil well enough? doubt it.

anyway, you have to gently rinse the roots to get rid of all the soil. a bucket filled is probably better than a faucet... don't use soft water, of course...

submerge and gently jostle the rootball. it'll slowly come free.. may need another bucket. may want a faucet to rinse a bit too. Be gentle, try to rip as few roots as possible. you will rip some... the finer hairs are going to suffer, inevitably.