From what I can see of it, the Categorical Converter is a complicated diagrammatic representation of various combinations of eduction and the square of opposition. I haven’t checked out all the details but, if it follows the standard rules, then the relationship between the propositions will be correctly delineated.
Logic is a little like the manual that comes with your computer. You need to know about 5% to deal with 95% of what’s necessary. The rest you can look up as necessary.
I like to keep things as simple as possible so that the account I give in the course is intentionally simplified (not falsified!) to avoid unnecessary detail and complication. For example, I state that conversion is invalid on A and O type propositions (excepting definitions). Standard accounts tell us that there is an operation called ‘Conversion by limitation’ which takes us from SAP to PIS (the limitation takes us from universal to particular and the conversion is as per normal). But there’s no need to have a special operation here. We can get from SAP to SIP by alternation on the square of opposition, and from SIP to PIS by (simple) conversion. It may take one step longer but we can also dispense with one extra rule.
Given my propensity to forget to check the Forum regularly, if you do start a new thread, drop me an email at firstname.lastname@example.org to let me know. That way, I can respond quickly.
I hope I’ve answered your question?