If you make your decision about whether to open the second box contingent on some fact about the future, then the contents of the first box let you predict that fact in advance. e.g., If the New York Yankees win their baseball game today then I will open the second box after their game, and if they do not win then I will not open the second box. Then if I open the first box and see $100, I can bet a lot of money on the Yankees to win, and if I see $0 then I can bet against the Yankees winning. If Omega is less patient then you'll need to pick something that resolves quicker.

 An FDT agent cannot really “die” as they do exist in all places of the universe at once. Whereas, as you have noticed, an observer can very much die in a finite thought experiment. In reality, there is no outside-text [LW · GW] dictating what can happen and you would just get quantum-immortaled into hell instead.

 This case is not really a scenario exposing a bug in FDT, it's rather FDT exposing an absurdity in the scenario's prior — stipulating that you should be only concerned with one copy of you (the one outside the simulation).

Thought experiments can arbitrarily decide that one copy of the agent does not correspond to an observer whose values should be catered to and therefore can be assigned a probability/utility of 0. But you, the one who implements the algorithm, cannot differentiate between yourselves based on whether they are simulated by Omega, only based on what you have observed.

Your choice doesn't change where you exist. In the situation which you describe, not opening the second box doesn't actually improve your situation (being simulated), and I would expect it to go the same way (being shut down).
I agree with the reasoning that you must be in a simulation, but I fail to see how your choice actually changes things, here.
You already exist in one reality (and potentially in a simulation), and you are only finding out in which one you are. So, isn't the only thing you are preserving by not opening the second box your lack of knowledge?
Opening the box doesn't transport you to a different reality, it just either means that your understanding of Omega was incomplete, or that you were in a simulation. But, if you are in a simulation, no matter how you decide, you still are in a simulation. 
(I must admit that I said yes without realizing the implications, because I didn't credit the omniscience sufficiently.)

I tell someone else that I got Newcomb'ed and that I will sell them the two boxes for X amount. Neither of us knows what will happen, since I actually won't open either box, but considering there is an omniscient Omega in the world, obtaining that information should be worth more than the money that may or may not be in the boxes. 
(To ensure that it doesn't count as opening the boxes by proxy, we settle on a fixed price. I think 250+ could be reasonably negotiated, both considering the value ranges known from Omega, and the potential value of the information.)

Then again, it may really not be a good idea to go out of bounds. 
(I quote "'Do not mess with time.' in slightly shaky hand writing."^^)
On the other hand, if Omega meant harm... Well, this is a longer debate, I think.

 If I am being simulated by Omega, then no matter what decision I make I am about to be terminated. Its not like 1 boxing makes the simulated me get to live a full and happy life.

Lets say Omega simulates 1 copy of me, and shows it $100 in box 1. If I have a policy of 1 boxing then that simulation of me 1 boxes, gets terminated (to no benefit to itself), then the real me gets the $100 due to the 1 box policy. If I have a two box policy the simulated me gets $200 before deletion, and the real me gets nothing.

So I agree with the 1 box policy, but at least to me the point of that policy is that it somehow transfers wealth between the simulated me that won't last much longer and the real me who might actually have a chance to benefit from it. I don't think the simulation benefits at all in any case.