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Wouldn't it be fair to distinguish between the baseline probability of any death, and the baseline probability of a death that could plausibly be suspicious, such as gunshot suicide?

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Sure, this was back of the napkin math and there will be plenty of ways to improve it. The problem is that the more details you add, the more difficult it will be to find actual numbers to put on these things as opposed to using the above actuarial tables if we lump all deaths together.

And for what it is worth, one of these deaths would be in the "suspicious" category and one wouldn't.

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