Compressor Stall-
Most "short field" procedures call for a climb at Vx untill obstacles are cleared then Vy. Am I to assume your short field has no obstacles since your climbing at Vy? In a Vx climb your betting your rear end that both engine keep working. A position I would rather not be in!!
Why are you raising the flaps with a positive rate of climb? Bringing up the flaps produces a pitch down moment which must be countered with a nose up elevator doesn't the airplane tend to sink slightly if you don't time the pitch correction correctly. If your retracting the flaps with a positive rate of climb wouldn't you be leaving ground effect at the same time? As you retract the flaps you are dumping some lift as well. As you leave ground effect you loss lift and increase drag. What performance and handling qualities are you experancing at this point? Where is the airspeed at this point? Some where between rotation and Vx (or Vy if thats what your using). It seems to me you might be setting your self up for something.
I highly recommend avoiding situations that require the use of a true short field procedure. The spacing between Vx and Vmc is small*, you are low to the ground, and high pitch angle if an engine fails in this position, it's all over but the crying. (*some twins Vx is below Vmc)
Here the FAA recommends using the manufacturers procedures, speeds and configurations. They read pretty much like this:
Positions the airplane for maximum utilization of available runway... Hold brakes... Add takeoff power... release brakes... Rotate at recommended Vr... Gear up with positive rate... Climbs at recommend speed and configuration or, in their absence, at Vx until obstacle is cleared or until 50 feet AGL... Establish pitch attitude to accelerate to Vy... Flaps up after clearing obstacle.
I agree you want to obtain as much altitude as quickly and as safely as possable. In normal takeoff climbs I use Vy or Vyse +10 (max) which ever is greater. The reasons are: (1) the pitch attitude at this point close to that of a single engine climb at Vyse (2) It allows for the swimming in glue affect (reaction & configuration time) (3) The amount of altitude differance between the two speeds is small and (4) If you do need to push the nose down to get to Vyse, you will lose less altitude becouse you didn't get very far from Vyse in the first place.
Fortunatly in most twins, Vy is above Vyse by about ten knots or so. Some one talked about the relation ship between Vyse and Vmc. Some twins Vmc is very close to Vyse and in others there is a wide spread. There is however a relationship between Vmc and stall speed. The certifcation requirement as I recall is that Vmc can not be greater that 1.2 Vs1.
I use to debate these techniques all the time with and old friend many years ago. We both had many engine failures and had flight tested many different techniques. In the end, we agreed to disagree. We continue to use what is best for ourselves. But it is fun defending our positions!!
By the way, I think Bob Hoover does the best conversion of altitude to airspeed and back again (on one and two engines) I have ever seen! To bad he retired the shrike.