vikena,
I knew that I could count on John_Tullamarine to come up with a worth-while reply during my jaunt.
On reflecting upon your query over the past few dats, I seriously cannot arrive at any solution to your problem other than to follow the steps laid down in my earlier post. OEI procedures and SIDs are incompatible in so many ways.
If you're really determined to see this through, and, seeing as you were speaking of very light 'positioning' weights, there is 1 rather crude, but safe way that you could achieve it.
You could dispense with the need to keep the 1st segment above the Runway / SID Gradient if you could achieve the required gradient all the way to acceleration altitude from 1st Segment performance. 1st segment performance assumes that the gear is down or in transit, and would be very limiting for normal operations, but, at the very light weights that you speak of, might be achievable. Of course, DO pull the gear up in actual operations.
If the MSA was not too high, about 2000 feet, you probably would not have a problem with the 5/10 minute limit at Takeoff thrust. Higher MSAs could see you hitting the limit.
You could use standard Newtonian physics to ascertain the time to V2 at Takeoff thrust and within the runway distance, the distance to Acceleration Altitude at the SID Gradient and TAS at V2 to find the time for the 2nd segment, and access 3rd segment data to ascertain the time to thrust 'cutback' to MCT. The total of these 3 times must be equal to or less than the 5/10 minute limit. Gross, not Net performance may be used for this, but Net performance is still required for obstacle clearance.
A small addendum to my earlier post, the Acceleration Altitude may be the lesser of the actual MSA, or that derived from the formula. The final +35 additive should be amended to +50 if there is a turning manoeuvre involved.
Other than that, I can see no other simplification possible.
At the end of the day, if you are going to operate a flight in accordance with OEI procedures in a SID, such a procedure must be within the constraints and approved procedures of your AOC, otherwise you'd be operating illegaly, even though safety may have been assured.
Regards,
Old Smokey