Is there any way to get power armor to a settlement without wearing it?

The easiest way to get a power armour to a settlement that I can think of, is to bring a companion to that power armour, make them equip the suit, and then dismiss them sending them back to the settlement you want the armour at.

It'll eventually turn up there, empty.

Yes.

Power armor frames need to be worn by someone to be moved, but it doesn't need to be you.

Have one of your companions wear it, then dismiss them and tell them to go to the settlement you want the armor at.

They will show up at the settlement, still wearing the armor. I've tested this a few times, on the Xbox One. I specifically recall it working with Piper.

However, in most situations this would probably be less convenient than simply donning the armor and moving it yourself.

If your concern is saving loading screens, and you have a bunch of suits at one settlement that you'd like at another, then this could actually help in that situation:

• Go to the settlement your companions are at.
• Tell them all to go where the armors are.
• Go where the armors are yourself.
• One at a time, have them get in and then tell them to go back to the other settlement.

All that being said, there's really no need to ever deal with more than two frames, unless you like them as decoration. As a result, I've never bought a frame from a store, and can't say what becomes of it.

Yes. With console commands.

When you find a suit in the wild, open the console and get its ID. They're usually followed by [EE] or [EP], or you probably have the wrong thing selected. Use disable and enable to see if you've got the right ID. Be sure to (re)enable anything you disable or you risk breaking your save.

Write the ID down.

When you get home, or wherever you want it, open the console and type prid (the suit's ID here, no parentheses). Now that it's your selected ID in the console, type moveto player.

I'm not sure how much this will preserve your sanity, but this is the only way I know of to move PA without anyone wearing it. The hardest part is finding where to click to get it selected in the console.

Fast traveling or using console commands are always going to be faster than using the GECK - unless I'm completely missing something here, it will still require restarting the game (or you know the console commands better than I do - the question's moot at that point, because there are ways to activate some mods while the game is still running, but that is way beyond my comfort zone).

Moveto should work on almost every item in the game, so that includes purchased frames. If all this console/breaking my save stuff scares you, then good, don't use it. These are some of the simpler tricks to do in the console and if you're unfamiliar using it, I'd advise against doing so on your main save until you are. E.g., do not confuse moveto player with player.moveto (moves: it-to-you and you-to-it, respectively).