Student or Learner
"If you would just agree to come to a party with me, I won't be talking to her. That's a promise." Correct?
"If you will give me a chance, I won't be drinking again." Correct?
If + will ... will is a fairly standard form used for negotiating, trying to reach agreements, etc. I think the first is more likely to find positive and negative views- it may be straining the system, but there's a definite logic to what the person is trying to say and it is the kind of thing people could use when talking, though the simple would work better than the progressive for me.
Extreme times may call for extreme grammar, and if this very mixed conditional saves a relationship, it might be worth ruffling a few traditionalists' feathers.