I'm really reluctant to rain on your parade but in the interest of knowledge....
If you have a screw thread in the back of your stamp, clamp it in a hole at the bottom of your arbor press or put it in the chuck on a drill press or failing all else, a pair of mole grips. This will give you some accuracy when lining up.
Using a blowlamp, heat the stamp to around 100degrees F , it'll only take about 30 seconds. Check with a digital thermometer.
Place your leather/foil in the right place and press the stamp for less than 1 second.