7-segment differences

JavaScript (ES6), 46 40 bytes

f=n=>n?+"452331541"[n%10]||f(n/10|0)+2:2

Alternative formulation, also 46 40 bytes:

f=n=>n?26523308>>n%10*3&7||f(n/10|0)+2:2

Edit: Saved 6 bytes thanks to @xsot.

Python, 50 48 bytes

f=lambda n:26523308-0**n*2>>n%10*3&7or f(n/10)+2

Explanation

This function operates on the least significant digit of the number n, summing the 7SD of the digits when incremented by one until after the first non-9 digit.

26523308 is a bitmask that encodes the mapping for the digits 0-8. When n=0, which only occurs when n comprises only 9s, the answer will be off by two. This is compensated by the expression 0**n*2. As for the digit 9, the bitmask evaluates to zero which will trigger the recursive call while adding 2 to the 7SD.

05AB1E, 31 30 28 27 26 bytes

Code:

9Ü©T%•2X›ùì•sè¹g®g-·¹Ú9Q·O

Explanation (outdated):

9Ü                              # Trim off trailing 9's
  ©                             # Copy this into the register
   T%                           # Get the last non-9 digit
     žh                         # Short for 0123456789
       •2X›ù앧                 # Compressed version of 4523315412
               ‡                # Transliterate

We are changing the following to the last non-9 digit:

0 -> 4
1 -> 5
2 -> 2
3 -> 3
4 -> 3
5 -> 1
6 -> 5
7 -> 4
8 -> 1
9 -> 2

For the special cases:

                ¹g              # Get the length of the input
                  ®g            # Get the length of the input with all trailing 9 gone
                    -           # Substract, giving the number of 9's at the end of 
                                  the input
                     2*         # Multiply by two
                       O        # Sum everything up
                        ¹Ú      # Uniquify the input
                          9Qi   # If this is equal to 9 (only 9's in the input)
                             Ì  #   Increment by 2 (_ -> 1)

Uses the CP-1252 encoding. Try it online!.

28 byte alternative: D[¤©•2X›ùì•sès®9Ê#¨]\rÚ9Q4*O.