Does this mining mechanic add genuine choice to my game?
Instead of modeling you can compute these results exactly. If you roll n dice at difficulty d, the variance will be [d * n * (d-1)/6 * (7-d)/6], and the mean net gain will be [d * n * (7-d)/6 - 1]. Both scale linearly with n, so here are the mean (measured in Net Gain Per Die) and variance for each value of d:

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| d | Mean | Variance |
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| 1 | 0    | 0        |
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| 2 | 0.7  | 0.3      |
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| 3 | 1    | 0.7      |
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| 4 | 1    | 1.0      |
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| 5 | 0.7  | 1.1      |
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| 6 | 0    | 0.8      |
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As you can see, there's definitely some actual choice here. 6 looks pretty useless (and 1 is entirely pointless - even if you didn't explicitly disallow it in the rules, no one would have reason to pick it), but the others are all somewhat reasonable and come in pairs - e.g. assuming you want the maximum average output (1 resource), do you want the lower variance that 3 offers or the higher one of 4? And are you willing to pay a little in expected output (down to 0.7) to get the extreme consistency of 2 or the extreme variance of 5? I'm not sure how much practical difference this will make to your game though; I'd have to know more about the game first and it'll also be a matter of opinion.