I've reached the point where I have the skills to really start putting some significant upgrades into my T-45 armor, but the materials required are still fairly precious. If I upgrade T-45, will I be able to transfer it to T-60 or higher?
No, the T-45 upgrades are not transferable to the T-60.
I have both, and have tried this. Additionally, if you remove the mods from the T-45 and look at them in your inventory, you'll see that they are labeled T-45.