If you can handle cutting aluminum that is 1/16 of an inch thick then you might consider making your own bracket. Here's what the bracket looks like in the car with and without the Palm III in it. I kept it pretty simple. This is my third attempt. The first one was pretty large. The second used the cradle. This one is smaller and easier to make.

To make this holder first get a pieces of 1/16 of an inch aluminum that is 9.5 inches by 4.25 inches. Next trace and cut out the pattern below. Next fold on the dotted lines so that it looks like the pictures above. Now round all the corners and smooth the edges. Finally paint it. I would suggest having the Palm handheld nearby so that you put the bends in the right place and to make sure everything fits correctly. Good luck.