onct (oncet) upon a time there were many strange variations on the spellings* (and pronunciations) of these numerical adverbs; twict (twicet) I have found entries now in the OED, which accompanying citations; e.g., 1934 C. Carmer "Chillun... think twict befo' yuh speak onct."

see, the thing about the OED is that it has a comprehensive descriptive history of our language up until about 1985, including much English and American dialect. (and if I can't find it there, I can always resort to DARE ;)

*(twaIs) Forms: 2–5 twies, 4 twyese, tweis, 4–5 twyys, tweies, 4–6 twyes, twys, Sc. twyss, 4 (7 Sc.) tuis, 4–7 twyse, twise, 5 tweys, 5 (6 Sc.) twyis, tuyse, 5–6 twis, Sc. tuys(s, 6 Sc. twyiss, tweyss, tuyss, tuise, 7 twyce, 5– twice; 6 twyst, 7 twist, 9 dial. twyste, twiste, 9– dial. twicet, twict.