If a 1" is too close, it is not to late to add an offset by notching the swing arm and welding back together like you did on the corners of your bumper.
How are you mounting the tire?
I think the 1" is going to be ok. I think it's too late to notch it at this point anyway, since I've got that diagonal in there already. Not that the angle grinder couldn't undo all of it...

But I did think of doing something like that before I built it, but I wanted the swing in-line with the bumper intead of standing out from it. In hindsight, I coulda shoulda woulda made the bumper out of 3x6 or something. I don't like the massive shelf some of the other aftermarket bumpers provide, but something in between wouldn't be bad...
Now that I've got the actual hinge pin installed and the swing mounted for real, it appears it's too close to the actual hinge on the door and hits. I may need to notch around that. Not a big deal. But before I do that, I am in the process of flame straightening the main beam because it warped a bit so the ends are a little closer to the body than the middle.
I've got an 8x8x1/4 plate that will be welded to the end of the tube and will have 3 studs in it. I'm also debating if I should bother having a hub centering tube piece or not. Just to make it easier to get it on and off. Could also use a tube through the center to make a bracket for something else in front of the tire, like the license plate, or I don't know what.
What is the advantage in your mind by removing the rear tire from the door and adding a bumper swing away?
Two swinging items are better than one?
First, to take the strain off the rear door hinge. I don't know exactly what they can handle, but I've read of some people talking about them failing. I likely will go to a 265/75/16 tire at some point, and planning for it now. Secondly, and more importantly, the tire will no longer be protected from below by the bumper. So if the spare takes a hit, I would rather all those forces not be passed directly into the door, it's hinge system, and the chassis... Lastly, I wanted to be able to carry some Jerry cans back there (instead of the roof), shovel, and axe, so I knew I needed some kind of carrier for that anyway.