Comment by int_19h
I kinda wish English avoided Xh type digraphs because they screw up common borrowings like Thai. Sure, that's not strictly phonemic in English, but I think realistically given how readily English adopts foreign words into it without completely nativizing them phonemically, any orthography should strive to reflect that, meaning that combinations like "th" should have their obvious meanings that can be inferred by native speakers even if such a sequence never occurs in native words.
Esperanto has a nice trick where they reserve "x" as a modifier letter, so if you can't use diacritics you write "cx", "sx", "jx" etc; but it does not have a sound value of its own and can never occur by itself. We could extend this to "tx" and "dx" with obvious values, and also to vowels - "a" for /æ/ vs "ax" for /ɑ/, "i" for "ɪ" vs "ix" for /i/ etc. Using "j" the way it is today feels somewhat wasteful given how rare it is. In the x-system it would probably be best represented by "gx", and then we could have a saner use for "j" like all other Germanic languages do. Which would free up "y" so we could use it for the schwa.
One thing that occurred to me the other day is that "x" is also a diacritic, so we could just say that e.g. "sx" and "s͓" are the same thing. Then again from a purely utilitarian perspective a regular dot serves just fine and looks neater (and would be a nice homage to Old English even if ċ and ġ are really just a modern convention).
Vowels, yeah... I think it's pretty much impossible to do a true phonemic orthography for English vowels that is not dialect-specific. As in, either some dialects will have homographs that are not homonyms, or else other dialects will not have the ability to "write it as you speak it" because they'll need to use different letters for the same (to them) sound. In the latter case, it would become more of a morphological orthography. Which would still be a massive improvement if it's at least consistent.
OTOH if you look at General American specifically, and treat [ə] and [ʌ] as stress-dependent allophones, then you can get away with 9 vowel characters in total (ɪiʊuɛəoæɑ). That's pretty easy with diacritics.