I've used a manual mill with a digital readout for capturing dimensions. The problem that I see using a probe is that the probe doesn't know the approach direction. In other words: if you're probing an edge that is 45 degrees from the machine axis, it only knows that it bumped into something, not where the true edge is.
Now that you've asked this question, I see a use for something that I just bought: a 3D Taster.
Here's what it does:
It works like a combination of a centering indicator and dial indiator. The probe tip goes in and out like a normal dial indicator. It also deflects in any direction and has a cam like a centering indicator. Both movements cause the needle to deflect.
Here's why it would be uniquely suited to what you're trying to do. The ball diameter is matched to the indicator. When you bump far enough into the part for the needle to read 'zero', the centerline of the gauge is exactly over the edge.
So there is no edge calculation needed like with normal edge finders. It works at any angle, from any direction--bump into the part, get to zero on the gauge and record the dimension.
I just found one on eBay:
Here is another brand of the same kind of indicator. They also have a couple of videos showing how it's used:
If you don't need that kind of resolution, you could also use a pointer in the spindle and just carefully dial to each location and record the numbers.
Do you know how to zero and set the Operator coordinates display on your Haas control?