Yes, there are plenty of ways to get a scrimmage. I usually use the Click Around the Map and Challenge the Online Teams Method (CAMCOTM). You seem to prefer the Fill Your Scrimmage List With Home and Away Challenge Method (FYSLWHACM).
I think having a Out of the Cup Tournament (OCT) might be a better way. Arguably more fun, too. But not more fun than making up acronyms.
I use the "click on manage my team, look at the right and pick the foreign team that's listed as needing a scrimmage, and challenge them to a game at their arena unless they're too good to let my scrubs get 48 minutes or if the timezone is one where I won't be able to watch the game" method.
Usually, at least. I occasionally accept the stray challenge that comes in before I can do all that.
I'll leave it as an exercise for the reader to rework that so it's suitable for acronymity.