Switching them around as you did:
would give you an invalid syllogism as it would fail rule 6. As you noticed, it also fails rule 2! Are you on the right track? Yes. You put the essential point very well – using your language, you can go from large to small (validly) but not from small to large.
Here’s an example of an invalid syllogism that fails only rule 6:
If you run the six rules over this, you’ll see that if passes the first 5 but fails no. 6.
If you start a new thread, email me at firstname.lastname@example.org to let me know.
Keep up the good work.