Is there a way to re-use the same settings, xy position, Z-probe, etc. and just carve again without having to go through all the setup steps?
First off I don’t use easel. I use the Universal Gcode Sender with Gcode created by other software. That said, you can save your Gcode( the instructions the router needs) in a text file. You can also set up simple fixtures to position your work for multiple pieces. These can be as simple as straight pieces of wood carpet taped or bolted down to the table. Then using the wood to position your work, and using the Gcode in Easel you should be able to do repeats. At worst, you may need to rezero your bit to the material.
Many folks here call what I would call a “Fence” a bump stop.
This gives you an idea of how to use a fence and clamps for positioning.
If you have just carved something using Easel, you have a mechanism in place to set the new stock in the exact same position, and new stock is the exact same thickness of the first one, all you have to do is install the new material and then hit the Carve button. When you get to the “Home” selection option, select the option for using the last Home position.
To add on what Brandon said, when you get to the Z probe select manual and that will keep the Z height the same, as long as its the same bit and you’re using the same thickness materiel.