We don't know. What's mentioned is informative, but certainly not decisive. Language is way too noisy for simple conclusions. E.g., spelling errors aren't exclusively based on phonetic similarity, and even if they were, their absence proves little.
The main thing we do not know is how regnum was pronounced. We know it was either of two options for interpreting gn and a third choice is that both were acceptable. People are also unsure how 4 of the short vowels sounded. Some say that they have slightly different sounds while others say that they are just short versions of the long vowels like the other two (A and Y). It is possible both variations co-existed.
We also know that western Romans often mispronounced Y as I since they had trouble rounding their lips for Y. Y had been introduced for transliteration of Greek loanwords, so it was not a native sound for the western Romans.
It sounds like something that should obviously have been done, but my naive googling isn't getting me anywhere so far.