I wonder - would it be effective to "shield" new members from reputation hits based on downvotes of their first question? Give them a little extra grace to work out what we're about here before sending them backwards? Or am I misunderstanding how this works so far?
You probably have misunderstood something. This thing you're describing here ...
their progression to more fully qualified members can be slowed, reducing their interest in persevering, [...] when their question is downvoted, as this reduces their reputation.
... isn't a problem but a feature. It is in fact exactly how things are meant to work.
Site privileges can be destructive in the hands of someone who doesn't know how to use them well or who doesn't understand how our site works. This is why they're gated behind incremental reputation barriers: you can only progress through them by contributing good quality content over time and demonstrating you understand how our site works. Over time you also see and learn how things like comments, edits, and closures and reopens work.
When someone doesn't understand how our site works, or is contributing low quality material, they are not yet ready for those privileges. They are also (not coincidentally) probably picking up some downvotes. This has the result of slowing down their progression toward privileges for which they aren't yet ready. If a user obtained those privileges anyway, they may cause trouble, and I or one of the other diamond mods would have to step in. I'd prefer they slow down and learn more over us having to do that.
So there won't be shields against downvotes and rep loss for new users. We need those mechanisms, both for the protection of our knowledge base, and for the protection of the new users themselves.