Chapter 2 of the Applied Quantitative Methods for Trading and Investment may be useful. You can download the excel file from the companion website.
Here is the link and the Download link is at the bottom: https://www.wiley.com/en-gb/Applied+Quantitative+Methods+for+Trading+and+Investment-p-9780470871348
You are right that it is a "very arbitrary procedure". More charitably it is a "hack" that gives a practical solution without addressing the fundamental issue.
The very fact that when you do an OLS regression of x vs y you get a different result than when you regress y vs x tells you that OLS regression is probably not the right tool to construct a hedged ...