The users seem determined to put the entire alphabet into the PUA, thus making a single character for <ng>, <kw>, <ii> etc. I would like to be able to present them with something that works and avoid this kind of catastrophe.
A better alternative to PUAs, which would require specific fonts and no interopable solution would be to use controls that make explicit grapheme clusters: ZWJ notably, and make sure that the editor handles it effectively as a single cluster, including for backspace.
Or, may be using existing combining modifier letters, even if they look like superscript in existing fonts (if you are ready to go to PUAs, you would need to develop a font for them), but as we don't know the whole extents of the "alphabet", it's hard to determine which solution is best.
I am assuming (I'm possibly wrong) that you'll need it to support some African languages, and if so, there are existing proposals to increase their support in Unicode with pending new Latin letters. Using PUAs could be an interim solution, before new characters are introduced, notably if you need combining modifier letters to act with the base letter as a single cluster.
If you need that to support the Latin transliteration of Native North American languages that you support on your web site, as a convenient tool allowing a reverse transliteration to the native script (which has constraints on its syllabic structure), and a convenient way to fix the Latin orthography in order to create richer contents transliterated appropriately and automatically into the native script, may be you need really a specific editor that can check and enforce the Latin orthography.
For example you cite the case of Pacific coast schwas, raised consonants and ejectives (like É kw qÌ), or Hawayian long vowels (with macrons, rarely supported in fonts) which are difficult to enter with existing keyboards and fonts. Using a more basic ASCII-based orthography seems like an input method for such languages, and an intermediate before the production of actual existing Unicode characters using the proper combining or modifier letters (in that case, Unicode itself is not the issue, and you may wonder how to create an input method editor which can show a "simplified" ASCII-only transliteration which can reliably be converted to the more exact orthography.

