In the first proof of concept draft of my reformed spelling proposal I ended up changing new -> noo to nu instead, because of a collision with traditional no. Later, when writing about the FOOT set, I thought about whether nuke should be spelled nook or nuuk.
This got me thinking about how to best represent in a reformed spelling the differences between American (and Canadian) English and British English as regards yod-dropping. Yod-dropping is a process where a word originally pronounced with a CUTE vowel comes to be pronounced with a GOOSE vowel instead. For example, suit used to be pronounced /sjut/ by most people (like saying the word you between the S and the T), but now the majority pronunciation is /sut/, and it is possible that the more conservative pronunciation will in time disappear entirely. It has happened with many other words before.
Going into a little more detail, yod-dropping is a historical process that has gone further in North America than in the the UK. So, while in the British isles yod-dropping happens in many accents after /tʃ dʒ j r Cl/ in every case, and after /s l z θ/ provided the j is in the same syllable as the preceding consonant (chew, juice, yew, rude, blue; suit, lute, Zeus, enthusiasm), in America and Canada it also happens after /t d n/ if the same condition applies regarding the j (tune, dune, new). There is some variation here, and it might depend on the specific word, but this largely applies.
How does this affect a reformed spelling? If the great majority of English speakers today pronounce a particular word with a GOOSE vowel because of a historical process of yod-dropping, it makes no sense to continue spelling it the way we spell the CUTE vowel. Etymology is a fascinating subject for some of us, but making spelling correspond to it is an exercise in futility (and in torture). If we are changing gnome to noem, I see no good reason why we should not spell chew, juice, yew, rude, blue, suit, lute, enthusiasm as choo, joos, yoo, rood, bloo, soot, loot, enthoozyazm. However, in the case of yod-dropping after /t d n/, and in the spirit of ekwanimity and pan-diialektalizm, why not a concession to the isles and a spelling tuun, duun, nu for tune, dune, new. After all, in the case of most English and Welsh (among others), they will have to deal with learning to spell the Rs they do not pronounce. To paraphrase John Wells, in a reformed spelling, we all have to make compromises.
To briefly show how this would affect the reform proposal as a whole, here is a text you are already familiar with, but with the above change. Words affected by it are in bold. Orange words are the same as in traditional spelling, red words are common “phonetic” respellings, and blue words are words that start and end with the same letter as in traditional spelling, and are otherwise one letter away from their traditional spelling, either because a letter was changed, or because a letter was removed. In a nod to etymological curiosity, I have underlined the words that I know to be the product of historical yod-dropping.
We hoeld theez trooths too be self–evidnt, that ol men ar kreeated eekwl, that they ar endowd bi thear kreeater with sertn unalyanabl riits, that amung theez ar liif, liberty and the persoot ov happynes. —That too sekuur theez riits, guvermnts ar instituted amung men, deriving thear just powers from the konsent ov the guvvernd, —That whenevver enny form ov guvermnt bekums destruktiv ov theez ends, it iz the riit ov the peepl too olter or too abollish it, and too instituut nu guvermnt, leying its fowndaashn on such prinsipls and organizing its powers in such form, az too them shal seem moest liikly too efekt thear saafty and happynes.
Proodens, indeed, wil diktaat that guvermnts lawng establishd shud not be chaanjd for liit and tranzyant kawzes; and akordingly ol experyans hath shoen, that mankiind ar mor dispoezd too suffer, whiil eevls ar sufferabl, than too riit themselvs bi abolishing the forms too which they ar akustmd. But when a lawng traan ov abuses and userpaashns, persooing invaryably the saam objekt evinses a deziin too reduus them under absoloot despotizm, it iz thear riit, it iz thear duty, too thro awf such guvermnt, and too proviid nu gards for thear fucher sekurity.