I pondered the same question briefly. The answer that leapt to mind works something like this:

What we tend to think of when we hear "oatmeal" is rolled oats. What I suspect is that you take oat groats and coarsely mill them (a la "corn meal"). "well beaten" may imply something closer to oat flour than Scottish Oats.

It appears the "Irish oats" are oat groats cut into bits. Scottish oats take Irish oats, steam them, then grind to meal with an optional bit of toasting thrown in. Oat flour is grinding much finer.

I think I'd go with Scottish oats. The cooking time will be moderately long, and they will ultimately thicken the broth, giving the porridgey texture.