You're sadly screwed here on multiple fronts. First off, although 240.4(D)(1) provides provisions for protecting 18AWG conductors, they can't be applied to a branch circuit due to 210.20(A)(4) of the National Electrical Code:
(4) Other Loads. Branch-circuit conductors that supply loads other than
those specified in 210.2 and other than cooking appliances as covered in
210.19(A)(3) shall have an ampacity sufficient for the loads served and shall
not be smaller than 14 AWG.
Furthermore, the "twin lead" 18AWG you refer to in your OP is either speaker wire, which isn't listed for 120VAC use to begin with, or a type SPT-2 flexible cord (lamp cord), which can't be used for permanent wiring due to 400.8:
400.8 Uses Not Permitted. Unless specifically permitted in 400.7, flexible > cords and cables shall not be used for the following:
(1) As a substitute for the fixed wiring of a structure
(2) Where run through holes in walls, structural ceilings, suspended ceilings,
dropped ceilings, or floors
(3) Where run through doorways, windows, or similar openings
(4) Where attached to building surfaces
Exception to (4): Flexible cord and cable shall be permitted to be attached
to building surfaces in accordance with the provisions of 368.56(8)
(5) Where concealed by walls, floors, or ceilings or located above suspended
or dropped ceilings
(6) Where installed in raceways, except as otherwise permitted in this Code
(7) Where subject to physical damage
Finally, the excess elbowing in your (PVC) conduit run violates 352.26:
352.26 Bends - Number in One Run. There shall not be more than the
equivalent of four quarter bends (360 degrees total) between pull points, for
example, conduit bodies and boxes.
In other words, this is what those funky "conduit body" things are for...