I think Wolfe is being tricky about the supposed "translation" of the whole solar series. The common language of the Whorl seems to dervived from English. We can tell because there are many plays on words in the BotLS that only work in English; for example, the chem soldiers call the wild animals of the tunnels "gods" and say that they reversed the word "dog."
The vernacular of Urth in Typhon's time is enough like Severian's language that he can time-travel there and communicate without noticing any problems. People of the Whorl can also astral-project to Severian's time and have no trouble in understanding the locals. Therefore it looks like everyone is using some form of English. The real "translation" would be to map new words for new creatures and items into archaic ones we can understand.