Course gamification: rewards that aren't bonus marks?
One idea is to include some problems/tasks in the final exam related to those competencies. This might not be possible.

A student who achieved the highest level in that competency automatically gets full grade on that question, and doesn't have to solve it (thus getting extra time for the rest of the exam). 

For levels 1 and 2 you can award free part marks, and the student gets either the free marks or his grade on the problem (whichever which is larger).

Added 

Depending on how long/short it needs to be, something like below might work (or could be terrible):

Exam:

Part A (short questions testing the competency parts)

Question 1 (competency A): bla bla bla

Question 2 (competency B): bla bla bla

Question 3 (competency C): bla bla bla

Question 4 (competency D): bla bla bla

Part B Actual exam, Questions 5- ...