Perhaps precommitting works here. It's a bad idea to make a rule "you must respect people's agency except when you really need to violate it". Adopting that rule would be beneficial in specific situations (like the one above) but generally would end in disaster.

If you instead make a rule "you must respect people's agency unconditionally", that rule is more practical. But you can't make that rule and then change your mind when you're in one of the rare situations where the other way happens to be better--if you did that, so would everyone else and you'd be screwed, on the average. So instead you precommit to following the rule and always respect people's agency, even when not doing so is beneficial.

It's a counterfactual mugging where instead of having to be the kind of person who would give Omega $100, you precommit to be the kind of person who would let his family die in this scenario because it benefits him in counterfactual scenarios. Thus, letting your family die here is ethical (although it may not be something people could realistically be expected to follow.)

(I don't believe this, by the way, because while you can't make a rule "respect people's agency unless you really need to violate it" you can have a rule that says "respect people's agency unless your excuse is good enough to convince a jury".)