Originally Posted by Private Jet
There isn't an "out" for all potential situations, and it's what the subject of risk analysis/management is all about.
Seriously?
Willy hit the nail on the head.
If you could get caught out as described, then your company should provide you with an escape plan.
GF and Icepack also raises a good point: depending on how far away from the airfield the first turn is, you will be well above the Engine out profile at that point so will have either excess speed to trade for height or if as GF suggests, you maintain V2 until you're in the clear.
Or... get a new SID designed. There must be others in your position.