triadruid

My biggest point of deviation from the first two answers you offer is that "can" is about ability for me, not about "getting away with".

Here's how I'd read those sentences:

What does "I can often not X" mean to you?
--> I might try frequently, but it usually doesn't work.

What does "I can not often X" mean to you?
--> It is rare that I am able to... (as in, the opportunity is absent)

What does "I often can not X" mean to you?
--> Most of the time, I am not able to... (the ability is generally absent)