Hi tilofr I can help you out with this one. The maths is built into our climbing calculator. First enter your climb: 1.3km and 5.5% (=> 72m rise): then your weight: then your climb type. I retrospectively put in your FTP from a guess (dont worry about this, its not needed for this calc). And the results…
with your baseline base power is 305 (4.16w/kg) you will get 4m 10s as you said (the calc actually says 308w 
To achieve 3:20s you would need a power of 399w (5.4w/kg) with 81kg
If you drop to 79kg you would need a power of 384w
Please see enclosed for proofs!
climb1|690x382
