Honestly, I'd just stick with the TN. With how easy a TN is to get, the only real advantage of a Green Card is if you plan on being unemployed in the US (which you don't, because you're in the US for the money like everyone else).
Though FWIW TN should allow you to work in the US anyway, so I'm not sure why they're only offering GC for relocation.
Be very careful about the strong USD, because things are more expensive in the US and they're often of lower quality for the same price. You won't feel richer unless you save a bunch of USD and move back to Canada down the line.
Earning CAD and spending CAD ~= Earning USD and spending USD
Earning USD and spending CAD is ideal