I agree with RIT Jared, 1-armed tire throwing does have an increased risk potential. If you want to do some throws, I'd stick with 2-handed variations like between-the-legs for height or distance.
You could smack it around with an aluminum baseball bat. It wouldn't have as much grip work as a sledgehammer, but the bat would let you do some funky 1-arm striking. Again, though, with 1-arm, watch the intensity.
You could also rig a rope attachment to the tire and...poof...instant sled dragging and the joys it brings.
I don't much care for the third one, carrying a plate in front. A - it's training static strength, which probably isn't a priority. And B - your front delts will definitely be a limiting factor. It's like isolation work meets G.P.P., and that's sad. Now, talk about something like a Zercher carry (with a bar in the crook of your bent arms), and you're good to go.
The other thing to remember with any walking or carrying movement, is to not always train in straight lines. Work diagonals. Try working sidestepping or backwards. More variety is more challenging, and more challenging is more productive.