Is there a rational reason to do this? Well, as I learned in China, being able to decipher street signs and place names is of enormous value when traveling in a country, even if your command of the language is poor. Learning a phonemic script can take a week or three for passable use, but learning a language can take years. Russian is a beautiful and elegant language, but realistically I am unlikely to learn more than a smattering of it at any time. Learning to read Cyrillic script in English may prove of value in learning to scan Cyrillic text generally, although it could plausibly increase errors in the decipherment of non-English text among people with a serious interest in learning a Slavic language.
Why would any English speakers write in Cyrillic? I imagine a lost Arctic island, New Sannikov Island, peopled by the descendants of illiterate English whalers marooned in the 17th century or later American prospectors, who only learned to read after a Ukrainian doctor washed ashore. They probably wouldn't write this way, though.
This script is geared most strongly to the Russian values for the letters, although many characters are used in different ways to represent the greater number of vowels of English. I also relied upon Cyrillic characters archaic in modern Russian, and the Cyrillic alphabet used to write Romanian before the 1860s. Romanian, as a Romance language, seemed like it would be an instructive example in using Cyrillic to write a non-Slavic language.
Most of the letters (АБВГДЖЗИКЛМОПРСТФЦЧШЫ) have common values in old Romanian and Russian. With some of the letters (ЕӖЙНУЭЮЯ) the Russian value is preferred. With others (ЅѸХѠЪѢѲ) I leaned to the Romanian sound. And I probably just made stuff up, too. Several of the characters from Romanian, such as Yat, are archaic letters that were reformed out of modern alphabets decades ago. The glyphs for the hard sign and such in Russian are here used for separate vowels.
This system should work reasonably well for transcribing my dialect, a western/mid-southern US dialect that merges lots of vowels, including "Mary-merry-marry," "cot-caught," and "pin-pen." It might work less well if you use more vowels. Dipthongs are represented with digraphs: эи, аи, ои, ѣу
Here are some samples, followed by some Benjamin Franklin quotes; I'll post some longer extracts when I get my keyboard for made-up languages finished.
Аи лыв ын Лѹъвъл, Кынтъки.
"Ѳъ Кѣт ын ѳъ Хѣт" ыз ъ бѹк баи Др. Соис.
Ѳъ рэин ын Спэин стэиз мэинли ын ѳъ плэин.
Ѳэир нэвър ѡъз ъ гѹд ѡор ор ъ бѣд пис.
Аи ѳинк ал ѳъ хэрътыкс аи хѣв нон хѣв бын анъръбл мын. …Ыт ыз нат ту маи гѹд фрынд'з хэръси ѳѣт аи ымпют хыз анэсти. он ѳъ кантрэри, 'тыз хыз анэсти ѳѣт хѣз брат ъпан хым ѳъ кэиръктър ъв хэрътык.
|А а||Az||"a" in "calm"|
|Б б||Bet||"b" in "bay"|
|В в||Ve||"v" in "vie"|
|Г г||Glagol||"g" in "gay"|
|Д д||De||"d" in "day"|
|Ж ж||Zhe||"zh", the sound in "J'ai," "vision," or "pleasure"|
|Ѕ ѕ||Je||"j" in "jay"|
|З з||Ze||"z" in "zoo"|
|И и||I||"ee", the vowel in "eat"|
|Й й||Short I||"y" in "you"|
|К к||Ka||"k" in "key"|
|Л л||El||"l" in "low"|
|М м||Em||"m" in "may"|
|Н н||En||"n" in "no"|
|О о||O||"o", the sound in "oak"|
|П п||Pe||"p" in "pea"|
|Р р||Er||"r" in "roe"|
|С с||Es||"s" in "see"|
|Т т||Te||"t" in "tea"|
|Ѹ ѹ||Uk||"oo," the sound in "foot," "pull," and "good"|
|У у||U||"oo," the sound in "ooze," "truth," and "boot"|
|Ф ф||Ef||"f" in "fee"|
|Х х||Ha||"h" in "he"|
|Ѡ ѡ||Omega||"w" in "way"|
|Ц ц||Tse||"ts" the sound in "pizza"|
|Ч ч||Che||"ch" in "cheer"|
|Ш ш||Sha||"sh" in "she"|
|Ъ ъ||Yer||"u" in "utter"|
|Ы ы||Yeru||"i" in "it"|
|Ѣ ѣ||Yat||"a" in "at" or "cat"|
|Э э||E||"e" in "ever"|
|Ю ю||Yu||"yoo" in "you"*|
|Ѳ ѳ||Theta||"th" in "thaw", "they"|