Running Pipe over Unheated Garage

I need to run some piping for living space above the garage. the space below is a 3 car unheated garage.

The space above will be heated. I'm wondering where is the best place to run water supply lines that need to run from one end to the other about 54feet to minimize freeze potential.

The piping will be pex for sure.

Choices are:

1.) Through Floor joists (ceiling of garage)
2.) Roof joists of finished space. 2x6 will have fiberglass batt insulation.
3.) Eave knee walls of finished space, also 2x6 with fiberglass insulation.

Any other tips? Should pipe be wrapped in insulation?

Probably better in the attic, as close to the ceiling as you can. The heat rises, so you want it close to the heated space. Insulation above it to help trap the heat.

I would say through the floor joists. Think about what temperatures are on both sides of where the pipe will be - the pipe will be between those temperatueres. One side is the heated space for all the choices. The other side is outside for the roof - that will be the coldest. Eve knee wall is also outside or possibly vented attic space. Even though the garage is unheated it has heated space on several sides and will be warmer than outside. Keep the pipes up as high as possible. Keep all the insulation below the pipes if possible or put as little as possible over the top of the pipes so they stay as close to the heated space temperature as possible. Make sure to air seal around pipes and wires so you don't have cold drafts through where the pipes are. I don't think insulation around the pipes themselves will help much.

None of them are "ideal" and the pipe may freeze in any of them. I would prefer in the ceiling of the garage. Very little of the heat in the house will gravitate downward, but the ceiling of the garage might still be warmer than the attic. Insulation will delay the freezing process, but unless the water is run periodically to "refresh" the temperature, it will still freeze, and then the insulation may delay the thawing process.

There is no attic. The ceiling is finished to the peak. Wouldn't call it vaulted, because it isn't tall.

Sort of like the second story in a small cape, that isn't dormered out. The sheetrock will follow the underside of the roof line.

I read somewhere about creating a "chase" or boxed in route for the piping and then "cheating" by heating that chase. The heating in this space will be forced hot air so it is possible to "pipe" in some hot air around these pipes. Thoughts?

INAP, but when I ran my supply over an unvented crawl space, I pulled up the subfloor and ran them so they'd be right up against the plywood, making sure to mark the heck out of where they were. The pipes haven't frozen.

If you put it on the living space side of the insulation, unless the heat goes out, regardless of whether it is high or low, you should be okay. If where it is is drafty, all bets are off! You want the room heat to be able to get to the pipes, so you don't want insulation between your source of heat and the pipes.