At least it is possible to force a single solution (discounting backtraces which is always possible) in 4x4:

  | 2 | 3 | 3 | 3 | 
  | 3 | 3 | 3 | 3 | 
  | 3 | 3 | 3 | 1 | 
  | 3 | 3 | 3 | G | 

I'm fairly sure the only solution here is 2 down to 3 right to 1 to goal. You can of course then use this to generate a couple of more by changing all the numbers that are impossible to reach.