I had never heard of Strine, but it sounds funny. It may not be the best example though. Strine is still written by English speakers, and its phoneme inventory, entropy statistics and so forth will be very similar to those of English. I even doubt if any of the statistical tools available to us would be able to pick up the difference between Strine and a standard Germanic language. Well it appears somewhat more "agglutinative", which might throw off the results when comparing word length distribution, but this will still be within the range of normal linguistic behavior.
If you want to argue that it could be a natural language rendered phonetically, I think it is a requirement that the scribe is not familiar with this language. This will often lead to reduced entropy. For example, if I had to transcribe spoken Chinese, I would miss all the tonal variation. I would probably also miss distinctions between sounds that don't exist in my native Dutch, so I would conflate them to something I do know. All this would lead to a reduction in the phoneme inventory and possibly a reduction in entropy. I'm doubtful that this extreme scenario would lead to any form of positional rigidity though.
If you want to argue that it could be a natural language rendered phonetically, I think it is a requirement that the scribe is not familiar with this language. This will often lead to reduced entropy. For example, if I had to transcribe spoken Chinese, I would miss all the tonal variation. I would probably also miss distinctions between sounds that don't exist in my native Dutch, so I would conflate them to something I do know. All this would lead to a reduction in the phoneme inventory and possibly a reduction in entropy. I'm doubtful that this extreme scenario would lead to any form of positional rigidity though.
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