Am I reading the cheat sheet right in that you have to calibrate the Haimer on every single machine startup!? I don't know why this would be necessary. I'm only familiar with one control (at least in the last two decades), but don't they all work pretty much the same when it comes to G54 and tool offsets?
The tool library on your control should be able to save far more tools than the carousel can hold, so you should only have to set the offset of each tool once until it wears out or breaks.
The process, from start to finish, goes like this:
1.) Load the Haimer probe into the spindle, assign it a tool number, and let the control know that it's a probe (not sure how to do this on Haas control, and might not even be necessary to assign it as a probe).
2.) Place your height setter on the table (table never goes away, but vises and fixture plates might), then touch off the Haimer to the height setter until both read zero. My height setter has fixed raised nubs next to the plunger to touch a probe off to, but it doesn't look like yours does. Somehow, though, you need to get the probe to read zero at the same point that the height setter reads zero (maybe stacking gauge blocks on the top of the setter's case until you have the correct height to touch off to).
3.) Place your workpiece in the the vise or fixture and touch off with the probe, storing X/Y/Z to G54 on the control.
4.) Insert tools and start touching them off to the height setter and storing the offset of each.
Done.
The reason steps 3 and 4 are in that order (at least how I like to do it) is that it offers a quick sanity check. After setting each tool offset, I can jog to the top of the workpiece (assuming G54 Z0 is the top of the stock) and see if the DRO reads 0 in Z.
From then on, you should only have to do step 3. Since both the probe's and the tools' offsets were measured from the same fixed point, you never have to change the tools' height offsets unless you put a new one in the machine or replace one that's worn. You never have to reset your probe's Z-offset because probes don't grow or shrink when not in the machine. As long as the control knows that, for instance, Tool 1 is your probe and Tool 1 is in the spindle when you touch off to your part to set G54, everything stays relative.
If I'm loading new tools into the machine, it's probably for a specific job, so I always load the stock in the vise and set my G54 first, then load the new tools in and touch them off. Doing it in this order allows me to more quickly perform the "test against the top of the stock" sanity check and make sure I didn't fumble when entering the offset.
My guess is that you're probably shaking your head and saying, "Yeah, yeah, of course that's what you do, but how do you do it on this control," and my apologies if that's the case. In my defense, I'm just reacting to the words "each time you power up the machine" on that cheat sheet. Surely there's a way to store the probe's Z-offset so you don't have to do that every time!