I'm realizing that my attitude towards heroic responsibility is heavily driven by the anxiety-disorder perspective,

Surprisingly, so is mine, yet we've arrived at entirely different philosophical conclusions. Perfectionistic, intelligent idealist with visceral aversions to injustice walk a fine line when it comes to managing anxiety and the potential for either burn out or helpless existential dispair. To remain sane and effectively harness my passion and energy I had to learn a few critical lessons:

• Over-responsibility is not 'responsible'. It is right there next to 'completely negligent' inside the class 'irresponsible'.
• Trusting that if you do what the proximate social institution suggests you 'should' do then it will take care of problems is absurd. Those cursed with either weaker than normal hypocrisy skills or otherwise lacking the privelidge to maintain a sheltered existence will quickly become distressed from constant disappointment.
• For all that the local social institutions fall drastically short of ideals - and even fall short of what we are supposed to pretend to believe of them - they are still what happens to be present in the universe that is and so are a relevant source of power. Finding ways to get what you want (for yourself or others) by using the system is a highly useful skill.
• You do not (necessarily) need to fix the system in order to fix a problem that is important to you. You also don't (necessarily) need to subvert it.

'Hermione' style 'responsibility' would be a recipe for insanity if I chose to keep it. I had to abandon it at about the same age she is in the story. It is based on premises that just don't hold in this universe.

but telling me that I am responsible for x doesn't tell me that I am allowed to delegate x to someone else

'Responsibility' of the kind you can tell others they have is almost always fundamentally different in kind to the 'responsibility' word as used in 'heroic responsibility'. It's a difference that results in frequent accidental equivocation and accidental miscommunicaiton across inferential distances. This is one rather large problem with 'heroic responsibility' as a jargon term. Those who have something to learn about the concept are unlikely to because 'responsibility' comes riddled with normative social power connotations.

, and - especially in contexts like Harry's decision (and Swimmer's decision in the OP) - doesn't tell me whether "those nominally responsible can't do x" or "those nominally responsible don't know that they should do x".

That's technically true. Heroic responsibility is completely orthogonal to either of those concerns.

I asked myself this because subsidiarity includes something that heroic responsibility does not: the idea that some people are more responsible - better placed, better trained, better equipped, etc. - than others for any given problem, and that, unless the primary responsibility-holder cannot do the job, those farther away should give support instead of acting on their own.

Expected value maximisation isn't for everyone. Without supplementing it with an awfully well developed epistemology people will sometimes be worse off than with just following whichever list of 'shoulds' they have been prescribed.