Morgoth, in fact, is around*. He returns to Angband in the episode immediately before the battle, and plays a major role in the climax (setting the spell of bottomless dread on Edhellos). So, if we want him to go back to the East, we'll have to have that explicitly happen at the beginning of the episode before the battle. Since we need him there afterwards to make dragons, that seems...unnecessary. We can send him back East in, say, Episode 11 if we want....
To sum up the train of thought here.
1) The Execs did not see a credible reason for Morgoth not to include balrogs in this battle. Why *wouldn't* he use his best available infantry in this attack down Sirion?
2) If balrogs are present and used in the battle, our 'balrog rule' means that a balrog must kill a named character.
3) The most expendable descendant of Finwë available at this time is Angrod (he has no major tasks left to complete), and so he was chosen as the victim.
If we want to preserve Angrod's death occurring in the Dagor Bragollach, then we need to convince the Execs on Point #1 above of a good reason not to send the balrogs into battle and have this force be 'just orcs'.
As for the published Silmarillion, I think it's fairly clear balrogs were not present. The narrator makes a big deal of pointing out that this battle demonstrated to Morgoth that orcs alone were insufficient to fight the Noldor. Ergo, no balrogs on the battlefield.
* I know Morgoth's timeline in the East is hazy. Here's the breakdown thus far:
Episode 2 - Morgoth departs for points east for a special secret mission project he's working on, something foretold in the Music.
Episode 6 - A solar eclipse occurs, and we get a glimpse of Morgoth on his newly constructed ziggurat with shadowy pseudo-worshipers.
Episode 8 - Morgoth returns to Angband. He puts the spell of bottomless dread on Edhellos (and other elves)