"Both a" vs "a both"
Solution 1:
You can avoid the problem by saying what is really behind your constructions:
This is a thing both natural and powerful.
But you might find this a phraseology too rhetorical and antiquated. It scans nicely, though.
Solution 2:
I believe both are technically grammatically valid, but I prefer the second, "both a," for a couple of reasons. First, as you say, it just sounds/looks better, perhaps simply because it's more often formulated with "both" first? I do think there's a slight semantic difference, too, or perhaps, better put, a difference in emphasis. Putting "both" directly after "is" emphasizes the sentence's focus on the description of the thing's dual nature, while putting "a" in between minutely breaks the rhetorical flow of the sentence, and to my eye throws a bit more weight onto the final "thing"--i.e. "This is a...thing."
Solution 3:
The meaning is slightly different here, even if it is just about emphasizing.
This is a (pause) both natural and powerful thing.
This is both (pause) a natural and powerful thing.
Imagine a discussion or talk about natural and/or powerful things. At the end of the discussion saying
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the 1. sentence emphasizes what it is, "natural and powerful". In this case you could leave "both".
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the 2. sentence emphassizes that it is "both". Here you could drop "a natural and powerful thing".
Of course this is a very little difference, but e.g. as the last sentence of a statement, this might tip the scales, if someone wants to point out the thing being both itself is most important, or it having the actual qualities.
In other contexts it might not matter at all, so there can but must not be a difference.