A question of interpretation: single word parenthesis

I disagree that these sentences are equivalent. To me, the first sentence is parsed like this:

Entity foo varies, seemingly at random.

ie seemingly refers to the randomness, not the variation. In the second, to my mind, seemingly refers to the variation.

In my mind, these two are more equivalent:

Entity foo seemingly varies at random

Entity foo varies, seemingly, at random

"Seemingly" can modify "varies" or "random". The distinction is less significant in this example but in other contexts it could matter more:

I am angry at random

I am seemingly angry at random

I am angry, seemingly, at random

I am angry seemingly at random

The relevant distinction is do I seem angry or am I angry at seemingly random times? The middle example appears the most ambiguous. For completeness, here are other ways of wording the sentences:

I seem angry at random

It seems I am angry at random

I am angry at random, it seems

The distinction between "angry" in these sentences also applies to "varies" in the original examples.