I wouldn't really go with that reformulation, because "impossible" is still a problematic term. I don't know that I'd say I think much is strictly "impossible".
You could potentially use "plausible" / "implausible" instead (implausible explanations should be eliminated in favor of plausible explanations). "Inconceivable" could also be a useful formulation. This may be roughly what you'd get with a generous interpretation of the original quote.
If you want, you could potentially also use "impossible" in the context of a specific model of reality, e.g. if angels don't exist, then it would be impossible for angels to do something. But this treats your foundational knowledge of reality as inviolable for the purposes of evaluating a specific claim, which may be a bit problematic if that claim undermines your foundational beliefs about reality (but it might also be useful if the "impossibility" of an explanation is supported by other evidence).
In any case, plausible/implausible could be considered some variant of Occam's razor / IBE. It's also related to coherentism, in that you can consider how well some explanation coheres with everything else you know about reality, favouring explanations that coheres more closely above ones that require additional claims, especially claims that seem like they should have far-reaching effects, and especially when we don't observe said effects.*
* Note that for, say, rejections of one scientific theory in favour of another, this commonly requires additional claims in any case, if there is some data that is contradicted by the current theory. We also accept that scientific theories aren't necessarily objective truths, but rather merely models reality as best we understand it, which carries a lower burden to warrant change. So, while favouring explanations that fit with what you already believe is extremely problematic if taken to extremes (as this might mean building an entire worldview around a false belief), there's also a question of how contrived your explanations need to be for this to work, and it's also reasonable to not keep adding claims and throw your entire worldview into disarray in response to every piece of data that can be explained perfectly well without any changes to a worldview.
The existence of angels may not be strictly impossible, but it's unfalsifiable, it has little to no coherence value (because they typically aren't posited to actually do much), and the existence of angels (of a particular religion) would arguably imply a lot more effects than a few lottery wins, and that might lead one to, say, the problem of evil / suffering, if that religion contains an all-powerful all-loving deity. An improbable event carries much less epistemic weight. Improbable things happen all the time.