The graph below is the results of a simulation using just the base game and King in Yellow mythos decks (permanent performance). The 3rd Act is very well balanced for this scenario.
For an average length game of 20-30 turns (and since King in Yellow doesn't include gate bursts, probably at the shorter end of this range), there's about a 1 in 8 chance that the 3rd Act will come up and force a loss by turn 20, 1 in 5 by turn 25, and almost 1 in 3 by turn 30. If you pay it off the first time it comes up - and 2 doom is usually less severe than losing 2 seals - then you are very rarely going to lose to it by turn 25, and even the chance by turn 30 is less than 1 in 10. Unless you expect a lot of delays, then it probably isn't worth paying it off twice.
Is it worth paying it off once? Against a 10-doom or a fast 11-doom Ancient One (Yig, Zhar, Rhan), probably not. The game is likely to be over before the third Act. Against anyone else, I'd probably pay it off if the first Act card comes up before 2 or 3 seals are down, and assume that I've time to get the other three seals anyway otherwise.
It doesn't take a lot to dilute it beyond relevance, though - adding only either the Dunwich or Innsmouth Mythos cards (about 35 extra) to the mix reduces the chance by 20 turns to 1 in 20, by 25 turns to 1 in 11, and by 30 turns to 1 in 7. It's still a risk, if the game drags on a bit, and if you got one in the first few turns it might be worth paying off just in case, but it's much less likely to matter. Add in any more than one large board expansion, and you might as well take the Next Act cards out altogether most games. Jacqueline Fine - since two doom is far more of a penalty than two clues - can also make the Next Act deck irrelevant.
Conversely, with the Visiting performance, you are guaranteed to have all 6 Acts in the top 27 cards, and so paying off at least the first 3 is essential. Going for a closing victory might be the best bet here, since those 27 cards only open gates at 7 locations, and a third of them open no gates at all. On the other hand, paying off 3 adds 6 doom, and there are two double-doom rumours around, both of which are likely to appear. They weren't kidding when they said it was for advanced players only!