I like my DIY4X tire carrier, but I would change to a swing down if I had to do it over again. One with the tire mounted toward the vehicle.
In my case if I get a flat I get the privilege of lifting a 37" Krawler up to chest high and trying to line the bolt holes up with the studs. On a swing down you can roll the tire and lean it down onto the studs. When removing take the lugs off, tip it up on edge and roll it where you need it. On a swing out you pull it off, back up, set it down, hopefully without it rolling away, or dropping it, or hurting yourself in the process.
Another thing I would do differently is mount the tire to the driver's side so you get better vision out of the rear view mirror. Mine is mounted near the center and blocks a lot of my vision. A come a long or hand winch on a boat could be used to raise and lower the tire carrier or even a spring like on some utiility trailer gates.