Using a comma after "that"

You use paired commas to set off a parenthetical.

Findings show that there is increased blood flow to the brain.

If you want to insert "during the initial stages of love" as a parenthetical, you set it off with commas, hence:

Findings show that, during the initial stages of love, there is increased blood flow to the brain.

This has nothing to do with the fact that the parenthetical happens to be preceded by the word "that". For example:

Findings show, during the initial stages of love, there is increased blood flow to the brain.

Findings show, during the initial stages of love, that there is increased blood flow to the brain.

Notice the commas are still there, still setting off the parenthetical. These are a bit awkward, but still perfectly legal grammatically.

Here's an example of a sentence that contains a parenthetical phrase (one that is not essential to the framing sentence): "Skye's sentence, which has no parenthetical phrase, needs no commas." Remove it, and the essential meaning of the sentence is preserved: "Skye's sentence needs no commas."

If you remove "during the initial stages of love" from Skye's sentence, you remove the condition essential to the findings, which leaves you with this meaningless statement: "Findings show that there is increased blood flow to the brain." So "during the initial stages of love" is not a parenthetical phrase.

I think the problem here is that "that" introduces a clause that is, in turn, introduced by a phrase. If it were an independent clause, one would separate any phrase before the clause proper with a comma. Thus: During the initial stages of love, there is increased blood flow to the brain. Now we are creating a noun clause by placing "that" in front of it. Does one then separate the whole phrase with commas, or just place one after "love"? Or does the rule of comma before a main clause not apply because it is now a dependent clause? I would argue for a comma after "that".