proteins themselves are turing complete; the folding is not really the interesting bit. just like there is a turing tarpit, trying to do anything reliable with protein folding (the process) is not likely to be effective. Instead, merely use existing functions provided by evolution to manage a DNA tape. You don't even need proteins; you can do it with just RNA and DNA. If you're really clever, with just RNA, and if you're super clever, just DNA.