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I've got a half-written reply to the original PSI thread, but for now:

On Mon, 29 Apr 2019 16:39:16 -0500, Aidan Aannestad <[log in to unmask]> wrote:

>> For the //n// -> [θ] thing you might do what Irish orthography sometimes
>> does and write both the underlying and the surface consonant: ‹nth› or
>> ‹thn›, at least if those don't occur as clusters, or don't in the relevant
>> context.
>
>That's an interesting thought, actually. It wouldn't work for the crazy
>deep orthography (<nth> would be ambiguous between /θ/ and /nɨθ/, but
>for an orthography that writes all the surface vowels, that could work
>well - there are no surface clusters of any kind. It's kind of clunky in
>terms of characters per segment, but that's not the end of the world.
>Irish for sure couldn't care less about that measurement!
>
>There's a couple of derived-only segments that would have to be
>exceptions (since they don't occur outside this morphophonemic context,
>so there's no premade letter to add for them), but non-double-spellings
><jh> and <wh> wouldn't be used for anything else, so it's probably not a
>big deal.
>
>OTOH if there were any native speakers, they might not care about the
>difference between derived and underived /θ/. It'd be hard to predict if
>they would or not.

<https://www.academia.edu/38201991/Orthography_and_phonological_depth.pdf>
is a paper which might allow you to make predictions about this sort of thing.  Snider, working in Lexical Phonology, claims that speakers want alternations represented in the spelling iff they occur in the output of the lexical phonology stratum, i.e. only postlexical process should be unwritten.  See in particular the "layman's guide" in the Conclusion (p. 19) for how to tell whether a process belongs or doesn't belong to this level, if you're new to lexical phonology (as am I).

Alex