How can I measure what is a relaxed geometry frame?

Stack and reach are consumer-friendly ways of doing what you're looking for, but are limited both by how widely adopted they are and to an extent how universally defined they are. A more foolproof way is to use any 2d CAD software. Model the bikes you know are working or not working for you. If you lack a record, or a record you trust, of any of the geometry, take a photo and get angle numbers that way, and just use a tape measure for lengths. Then you'll be able to model other frames/bikes and see if the position options they offer will work.

One of the tricks to doing this is answering the question of whether you can recreate your saddle setback but without having, or needing to create, an accurate model of your saddle and seatpost. Everything else is easier to express as a bunch of lines, but knowing whether you're going to be able to get the exact fore/aft position you want relative to the BB center when you're looking at bikes with different seattube angles in practice sometimes requires a measured guess of whether there's a post out there that does what you need, and then a willingness to buy that post. This comes up with Brooks a lot, where getting them far back enough can be difficult.

Use a very basic CAD software. It's easy to find one where the learning curve is steeper than necessary for this purpose. You just need some angles, lines, and circles.