This was the hardest day-one challenge that I've ever seen in AoC. Hopefully the others don't follow suit!
My solution uses a hybrid of Regex matching and in-code pattern matching. Regular expressions are used to extract individual digits / "digit words", and a switch expression converts any resulting words back into digits. Everything is kept as a string until the two digits are concatenated, and then the final calibration value is parsed into an integer.
I handled part 2 by using an obscure feature of .NET's RegEx engine - the RightToLeft option. This causes the engine to search the string in reverse, from end to start. Processing the input in this way ensure that we get the other part of any overlaps, with the expense of an entire second pass. Once for the left-to-right read, and again for right-to-left. Not very efficient, but simple and effective!
Also, I totally got stuck on what turned out to be a copy-paste error:
