I think on reflection I shouldn’t have compared this usage to てもいい so directly, since Doraemon’s ultimately just talking about himself with 聞かれて. I don’t think you would give permission (or the reverse) with the passive like that.
But I do think of てもいい as the same as the “even if” ても, ultimately, even if (har har) it would be awkward to translate it that same way in English all the time.
What’s tricky I think is just how much what’s said implies about the flipside of the coin.
“even if you ask me all at once, I’ll have trouble (answering)” definitely implies that if it weren’t asked all at once, he’d still have trouble answering (and implies that asking all at once would help in some way which doesn’t really make sense to me but I guess could to Doraemon).
My gut is that Doraemon would be fine with answering them one-by-one (although when that does happen, he comedically disregards them or gets distracted), or just going ahead without answering any questions at all, and that getting asked all at once is what’s giving him trouble, not a possible solution.
And my gut also is that ても doesn’t inherently imply as much about the flipside as “even if” does. So that gels with my read on the situation in that way. Like to my gut, the flipside implications of “even if” definitely trump situational context, but the flipside implications of the situational context trump those of “ても.”
But my gut could certainly be wrong. Maggie-sensei’s answer there does more work getting the sentence to where the “even if” makes sense (if Doraemon literally said “I won’t be able to answer them right away” instead of こまる the “even if” would be a slam dunk since the flipside implication would be totally acceptable, since the “all at once” would clearly help with “right away”), and her gut is surely more honed than mine, so it may just be I’m understimating the weight of the も’s implication here (but I’m not positive).
I was curious to find other examples, so I tried searching for a clearly bad thing + temo + こまる with “死んでも困ります,” and I found an example from a March 2020 article:
and while I don’t really agree with the larger point that was being made (especially in hindsight), it’s maybe a good example since I feel like it’s definitely not saying “even if the economy dies, that’s bad for us.” It’s more like pointing out the economy dying is another possible danger.
Whereas if 死ぬ was something awesome, the “even” sense would be very strong with the same construction.
So I figure ても’s always “if X then Y,” it’s just the specifics of X and Y that informs the nuance of if it’s “even if X then Y,” “also if X, then Y,” or more neutral. (and the Doraemon example feels off-hand and neutral to me).