Would it make less room for tension if second-time closure was performed by another moderator?
Unfortunately no. Both your examples seem to focus on the moderator closing the question rather than whether the questions should be closed or not, I'd say that tension is build in them and it wouldn't make any difference if it was another moderator closing the second time. Worth noting however that other than a handful of passive aggressive comments, the community seems to agree with the closures on both examples, and in the second case the question was re-opened after it was improved - I call that a win.
Generally speaking, it might make sense for a different moderator to close the second time, even if only for appearances sake. But, as kiamlaluno already mentioned, the people who'd concentrate on the moderator closing the question instead of the actual merits of the question would probably also be very quick to liberally accuse the moderators for covering for each other, and we'd be back where we started.
I see only one "solution": If your question was closed, concentrate on discussing the question itself and not the close voters, regardless if there was a moderator involved or not. It's extremely simple really, come on Meta and ask:
Hey, can someone explain to me why this question is off topic / not constructive? Is there anything I could do to improve it?
That's all, if you are doing anything different you're doing it wrong. A closed question is just that, closed, there isn't any difference if it was closed by five community votes or by a moderator. And there's absolutely no gain for the community - other than a pint of entertaining Meta drama - if you concentrate on anything else but how the question could be improved and re-opened.
Here's a very recent example of Meta awesomeness - the system works!