In general, for cold climates the best moment to transplant is when the soil temperature starts to rise about 10 ºC --> 50 ºF.

Where I live the ancients, they made a deep hole until to find clay. Sometimes this hole achieved 5 meters or more à 16.5 feet, they made that to fight against the dryness.

I think that the best advice to transplant it will be made by people that grow figs in the similar environments.

Also consider do not transplant it into the ground, may be better into a bigger pot.

In the cold climates when the tree is growing into the ground, it needs a good protection against the cold; there are many posts about this in this forum.

In general is safe to transplant after the leaves have fallen ,that is when the plant goes dormant.The garage is a safe place to store your fig, you can cover it with an old blanket for added protection.It is also a good idea to give your new transplanted fig a cup of water once a month.Some people like to transplant their figs in early spring ,either way works fine.Ciao
Giuseppe