a seemingly infinite amount of points in the "Bad events I have personally caused" category on their scoreboard

Perhaps that is how some people who prefer TORTURE to DUST SPECKS are thinking, but I see no reason to think it's all of them, and I am pretty sure some of them have better reasons than the rather strawmanny one you are proposing. For instance, consider the following:

• Which would you prefer: one person tortured for 50 years or a trillion people tortured for 50 years minus one microsecond?
  • I guess you prefer the first. So do I.
• Which would you prefer: a trillion people tortured for 50 years minus one microsecond, or a trillion trillion people tortured for 50 years minus two microseconds?
  • I guess you prefer the first. So do I.
• ... Now repeat this until we get to ...
• Which would you prefer: N/10^12 people (note: N is very very large, but also vastly smaller than 3^^^3) tortured for one day plus one microsecond, or N people tortured for one day?
  • I am pretty sure you prefer the first option in every case up to here. Now perhaps microseconds are too large, so let's adjust a little:
• Which would you prefer: N people tortured for one day, or 10^12*N people tortured for one day minus one nanosecond?
  • ... and continue iterating -- I bet you prefer the first option in every case -- until we get to ...
• Which would you prefer, M/10^12 people tortured for ten seconds plus one nanosecond, or M people tortured for ten seconds? (M is much much larger than N -- but still vastly smaller than 3^^^3.)
  • I am pretty sure you still prefer the first case every time. Now, once the times get much shorter than this it may be difficult to say whether something is really torture exactly, so let's start adjusting the severity as well. Let's first of all replace the rather ill-defined "torture" with something less ambiguous.
• Which would you prefer, M people tortured for ten seconds, or 10^12*M people tortured for 9 seconds and then kicked really hard on the kneecap but definitely not hard enough to cause permanent damage?
  • The intention is that the torture is bad enough that the latter option is less bad for each individual. I hope you still prefer the first case here.
• Which would you prefer, 10^12*M people tortured for 9 seconds and then kicked really hard on the kneecap, or 10^24*M people tortured for 8 seconds and then kicked really hard on the kneecap, twice?
  • ... etc. ...
• Which would you prefer, 10^108*M people tortured for one second and then kicked, or 10^120*M people just kicked 10 times?
  • OK. Now we can start cranking things down a bit.
• Which would you prefer, 10^120*M people kicked really hard on the kneecap 10 times or 10^132*M people kicked really hard on the kneecap 9 times?
  • That's a much bigger drop in severity than I've used above; obviously we can make it more gradual if you like without making any difference to how this goes. Anyway, I hope you still much prefer the first case to the second. Anyway, continue until we get to one kick each and then let's try this:
• Which would you prefer, 10^228*M people kicked really hard on the kneecap or 10^240*M people slapped hard in the face ten times?
  • You might want to adjust the mistreatment in the second case to make sure it's less bad than the kicking.

... Anyway, by this point I am probably belabouring things severely enough that it's obvious where it ends. After not all that many more steps we arrive at a choice whose second option is a very large number of people (but still much much much smaller than 3^^^3 people!) getting a dust speck in their eye. And every single step involves a really small decrease in the severity of what they suffer, and a trillionfold increase in the number of people suffering. But the chain begins with TORTURE and ends with DUST SPECKS, or more precisely with something strictly less bad than DUST SPECKS because the number of people involved is so much smaller.

To consider TORTURE worse than DUST SPECKS is to consider that at least one of those steps is not making things worse: that at some point in the chain, having a trillion times more victims fails to outweigh a teeny-tiny decrease in the amount of suffering each one undergoes.

I am a little skeptical, on general principles, of any argument concerning situations so far beyond any that either I or my ancestors have any experience of. So I will not go so far as to say that this makes TORTURE obviously less bad than DUST SPECKS. But I will say that the argument I have sketched above appears to me to deserve taking much more seriously than you are taking the TORTURE side of the argument, with your talk of scoreboards.

Do unto others as you would have done to yourself

This is a pretty good principle; there's a reason it and its near-equivalents have cropped up in religious and ethical systems over and over again since long before the particular instance I think you have in mind. But it doesn't deal well with cases where the "others" vary hugely in number. (It also has problems with cases where you and the others have very different preferences.)

I, for one, would rather have a dust speck in my eye than be tortured for 50 years. And I wouldn't get 3^^^3 specks of dust in my eye, because none of them did either, they only got one.

This reasoning would also suggest that if you have to choose between having $10 stolen from each of a million people and having $20 stolen from one person, you should choose the latter. That seems obviously wrong to me; if you agree, you should reconsider.

engulf the Earth and possibly most of the Milky Way

You are vastly underestimating how big 3^^^3 is.

I choose to save the person in front of me, and fix any negative results afterwards

That sounds very nice, but if you are unable to fix the negative results this may sometimes be a really terrible policy. Also, in the usual version of the hypothetical the dust specks and the torture are not different in "remoteness", so I don't see how this heuristic actually helps resolve it.

somebody figured out the answer to this dilemma about 2000 years ago

It is not, in fact, the same dilemma. (E.g., because in that scenario it isn't "one person getting something very bad, versus vast numbers getting something that seems only trivially bad", it's "one person getting something very bad, versus quite large numbers getting something very bad".)

If you would like a religious argument then I would suggest the Open Thread as a better venue for it.

Anyway, I think your discussion of harming A in order to help B misses the point. Inflicting harm on other people is indeed horrible, but note that (1) in the TvDS scenario harm is being inflicted on other people either way, and if you just blithely assert that it's only in the TORTURE case that it's bad enough to be a problem then you're simply begging the original question; and (2) in the TvDS scenario no one is talking about inflicting harm on some people to prevent harm to others, or at least they needn't and probably shouldn't be. The question is simply "which of these is worse?", and you can and should answer that without treating one as the default and asking "should I bring about the other one to avoid this one?".