Hello @Bobby_Goldner
Splitting the curve stroke geometry into a separate subtool by any method will delete the live curve from the stroke geometry in the resulting subtool.
If, however, you split the curve stroke into a separate subtool via the “Split Hidden” or one of the “Split masked/unmasked” functions, the curve itself will remain live in the original subtool, so you can reposition the curve and apply the stroke to the curve again. You can create as many different mesh variations as you like doing this.
In order to hide sections of your mesh, you should be familiar with the mesh visibility functions.. It would also make it easier if your target mesh was a single polygroup. The curve geometry can be hidden with a single shift-ctrl click on the target mesh in that case. If your polygrouping is more complex than this, consider duplicating your target subtool and polygrouping the entire mesh as a single polygroup, helping you quickly split off curve strokes while preserving your original polygrouping in the original subtool.