What to do with old connections when moving outlet to dedicated circuit?
Of the three options you mention, the first is fine; leave the wires in the box, spliced.

The second, no good at all. Splices must be in an accessible box.

Third, also fine. You can certainly blank up the existing box and run new.

I prefer a fourth option; Leave the existing receptacle alone and run a new circuit to a new box. WHY do you need the existing one removed?