All the options you suggest seem to conform to post-2014 Code, but there are important additional requirements for each (see below).
First, you are installing an "Equipment Grounding Conductor (EGC)", the important safety feature that routes fault current back to the electrical service connection in your electrical box (not to earth ground), so a breaker will trip and disconnect the fault. You don't want this new safety feature to be accidentally disconnected in the future, leaving the outlet unprotected without any visible notice! Thus, you should make it as clear as possible to future workers that this is an EGC and they should not cut or disconnect it at any point along its length.
2014 Code Language:
250.130(C) Nongrounding Receptacle Replacement or Branch Circuit Extensions. The equipment grounding conductor of a grounding-type receptacle or a branch-circuit extension shall be permitted to be connected to any of the following:
(1) Any accessible point on the grounding electrode system as described in 250.50
(2) Any accessible point on the grounding electrode conductor
(3) The equipment grounding terminal bar within the enclosure where the branch circuit for the receptacle or branch circuit originates
(4) An equipment grounding conductor that is part of another branch circuit that originates from the enclosure where the branch circuit for the receptacle or branch circuit originates
(5) For grounded systems, the grounded service conductor within the service equipment enclosure
(6) For ungrounded systems, the grounding terminal bar within the service equipment enclosure.
Connect to water pipe: While option 250.130(C)(1) above to connect to the Grounding Electrode System (your bonded water pipe in this case) is allowed, the connection back to your electrical box (not earth ground!) is indirect and any future failed/removed segment or bond along that path (e.g. replaced pipe or broken bond wire in crawl space) will leave your outlet unsafe without anyone knowing that. I would avoid this option.
Connect to EGC from other circuit: This is the best option IMHO. However, the type of cable/wire used requires thought, because there are additional Code requirements for each type.
An earlier Question/Answer suggested using bare-ground Armored
Cable (spiral armor with a real bare copper ground wire inside) for
this purpose, as it makes the issues below easier. You use it with
MC/AC-type fittings. Earlier related Question
If you run Romex, (250.120(A)"where it [EGC] is a wire within a
raceway or cable, ") you need to follow all the rules for running
cable - proper terminations, listed clamps and fittings, support
intervals, physical protection depending on where it is run, etc. You
also should make it clear to future workers that the hot and neutral
inside are not in use, but the ground IS.
If you run THHN or bare ground wire, you need to follow the rules
for running an Equipment Ground Conductor on its own. 250.120(C)
notes "(C) Equipment Grounding Conductors Smaller Than 6 AWG:
Where not routed with circuit conductors as permitted in 250.130(C)
and 250.134(A) Exception No. 2, equipment grounding conductors
smaller than 6 AWG shall be protected from physical damage by an
identified raceway or cable armor unless installed within hollow
spaces of the framing members of buildings or structures and where
not subject to physical damage." Bare ground AC covers the protection issue.