What you are describing is rather unusual with a neck bow moving up and down the neck. Keep in mind that the truss rod and strings both put tension on the neck - theoretically in opposite directions. But see below because your Godin may have a truss rod that can defy the opposing tension theory and possibly account for this unusual behavior.
From what you have shared - two things come to my mind. It is likely that your guitar has been subjected to an environment with low relative humidity (common during winter heating season) which often will cause a bow in the neck due to drying of the wood.
The other thing to be aware of is that according to the Godin website, all Godin guitar necks are equipped with a DOUBLE Action truss rod. Most guitars have a single action truss rod which counteracts the string tension to lessen the bow (or relief) that is caused by the string tension. Loosening a one way truss rod will relax the neck and allow it to bow under string tension but will not cause it to bow in the absence of tension.
A two way adjustable truss rod (or double action) like the ones found on Godin guitars and a few others actually will bow the neck if turned one way and bow the neck in the opposite direction if turned the other way. So you might say you can "tighten it" in BOTH directions. One direction causing a bow, the other direction causing a back bow - with or without string tension.
This could account for your observation of a bow showing up in different places after turning the truss rod in alternate directions. It is also important to understand that the guitar's reaction to a truss rod adjustment may be gradual and the neck may continue to respond for a period of time after the adjustment is made.
Here is a picture of how the Godin double action truss rod works from the Godin webstite Double Action Truss Rod - Godin guitars
Before doing anything else - if your guitar is under warranty, you may be able to take it to an authorized Godin repair tech and have them repair it under warranty. My Taylor guitars have a lifetime warranty to the original owner. Or even if it isn't under warranty please make a phone call to Godin to see if they will offer support over the phone.
If you are unable to get any support from Godin - you can take your guitar to a local recommended guitar repair technician or luthier whom you can trust - or you can follow my recommendations below.
You are probably doing the right thing by re-hydrating your guitar. Shoot for about 55-60% relative humidity during the re-hydrating (re-humidification) process and once stabilized, try to maintain around 50% if you can.
While re-hydrating your guitar, I would loosen the strings and then adjust your truss rod until the neck is straight with no string tension. Use the chart in the link to determine which way to turn the truss rod to achieve this. Remember, don't turn too much in either direction because the double action truss rod will actually exert tension on the neck in both directions.
During the re-hydrating process you will probably notice some movement in the neck as the wood absorbs moisture. After a few days of re-hydration your guitar should stabilize and the neck should stop moving. Once you are sure your guitar is fully re-hydrated - add tension back to the strings and adjust the truss rod to provide the desired amount of relief and hopefully you will be back in business.
To those who might fear that relieving string tension will hurt your neck - that is a myth and totally without merit. I have four friends who are luthiers (build and repair guitars). They often have guitars in their shop where the strings are off the necks for a week or more. How else would you do a re-fret? If you are skeptical about this - call or visit any luthier.