Isn't the experience of hundreds of players who have upgraded their plot size via relocation in the past 2 years proof enough for you?
The Shirogane Housing and Relocation article on Lodestone is probably as close to "official" proof as you'll get though you notice it doesn't go into great detail.
https://na.finalfantasyxiv.com/lodes...0dd62c3c50fc74
Get your permit now. Not only will you save gil in the long run, it will allow you to avoid losing your plot to demolition while you wait for a medium to become available. You can't enter the house to reset the demo timer when you haven't built the house in the first place.
Whether you want to buy and use small exterior fixtures/skins now depends on marketboard prices or if you're going to get the fixture crafted. Anything you're crafting will definitely be cheaper if you make the small size. If you're buying off the marketboard, prices get weird sometimes and medium can cost less than small so shop around.
If you're getting small fixtures/skins to save money, make certain they are applied to your house before you relocate. Only the active fixtures will automatically change in size when you relocate. Things in your inventory will not.