W/out knowing your riding fitness level, I'll take a stab.
The climb up Hamilton from the west isn't that tough. Gentle grade, etc. Doing a search on this board will give you a lot of ride reports.
From the summit, to the junction, is an easy ride. It's mostly downhill, yet there are several inclines. Nothing too hard.
Yes, there are some cattle guards. Just ride in a straight line over them. I know some riders that "bunny hop" them. I just ride over them myself. If you're uncomfortable riding over them at a high rate of speed, then slow down a bit.
Refill your bottle (and tummy) at the Junction Cafe. As you know, since you've done this drive in your Miata, there are a few hills coming up. Again, nothing too tough to handle. The rest of the ride is downhill.
Depending on the time of year or even the time of day, you may experience and westerly wind blowing into the canyon. This may impede your downhill speed, making you work a bit more.
It's a good ride. Have fun,
BR