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This is a challenging problem indeed. I thought I had worked out that the chance of a single line containing the requisite combinations of letters as about 18%, but when I tried to verify by simulation I found out that the actual value is likely to be a little more than twice that.
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The simulation is correct. I showed in
this post that this value is about 39.84%. It is the value that I refer to as 1 - P. I derived P by inclusion-exclusion, which gives a fairly simple expression.
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Over all, I think that the chances of one of 154 monkey-sonnets qualifying is in the neighborhood of 0.04%.
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Right, I got 0.039%.