From the AIM
2. ODPs and SIDs assume normal aircraft performance, and that all engines are operating. Development of contingency procedures, required to cover the case of an engine failure or other emergency in flight that may occur after liftoff, is the responsibility of the operator.
From AC 120-91
7. TERPS CRITERIA VERSUS ONE-ENGINE-INOPERATIVE REQUIREMENTS.
a. Standard Instrument Departures (SID) or Departure Procedures (DP) based on TERPS or ICAO Procedures for Air Navigation Services—Aircraft Operations (PANS-OPS) are based on normal (all engines operating) operations. Thus, one-engine-inoperative obstacle clearance requirements and the all-engines-operating TERPS requirements are independent, and one-engine-inoperative procedures do not need to meet TERPS requirements. Further, compliance with TERPS all-engines-operating climb gradient requirements does not necessarily assure that one-engine-inoperative obstacle clearance requirements are met. TERPS typically use specified all-engines-operating climb gradients to an altitude, rather than certificated one-engine-inoperative airplane performance. TERPS typically assume a climb gradient of 200 feet per nautical mile (NM) unless a greater gradient is specified. For the purposes of analyzing performance on procedures developed under TERPS or PANS-OPS, it is understood that any gradient requirement, specified or unspecified, will be treated as a plane which must not be penetrated from above until reaching the stated height, rather than as a gradient which must be exceeded at all points in the path. Operators must comply with 14 CFR requirements for the development of takeoff performance data and procedures. There are differences between TERPS and one-engine-inoperative criteria, including the lateral and vertical obstacle clearance requirements. An engine failure during takeoff is a non-normal condition, and therefore takes precedence over noise abatement, air traffic, SIDs, DPs, and other normal operating considerations.
I don't fly 135, and had just a skosh, at best, about 11 years or so ago.
I've read, and re-read your posts and the above several times.
We used to use a Part 142 school at my previous airline, and flew a model of airplane certified under a SFAR since it needed a 5 segment climb to be legal. (Yeah, I know, right.....
Here's what I get out of all of the information you've posted, adding to it other junk accumulated in the grey matter over the years.
1) ODPs, as published, are required 2 engines.
2) If you blow a motor, the operator is required to come up with an alternate procedure.
Now, every one I know plans to reject every takeoff. Then when you hit V1, you plan to lose the most critical engine.
Why do they make ODPs and SIDS (besides the side effect of organizing outbound traffic to the departure gate)? To either a) Not hit stuff b) not waking up NIMBYs.
If it's number (b), and you lose a motor, tough cans alice. Wake up and deal. You are in an emergency situation and need to do what you can do to have a safe outcome.
For (a), as far as I can tell, you have 2 choices. 1) To ensure the airplane can, one engine down, make the performance. If the airplane can make the performance, the operator has a valid procedure - making the required ODP performance.
2) The airplane can't make the ODP/SID gradient OEI, then the operator needs a tailored OEI departure procedure.
Those are the only two options I can think of.
The other thing that people love to forget in these academic arguments is that all takeoff performance ends at 1500 AGL unless otherwise noted, as the data gets you to traffic pattern alt and a box pattern to land is the practical application.
Sure you can take a look at your OEI ceiling for the weight of the plane at take off and make a guess that you'll be able to climb up there. However, you have no data on how long it will take, so there is no terrain clearance.
All airports need some sort of area. There are some airports, out west especially, that are in bowls or are one way in and one way out. In that case, you'd better make sure your plane can make the turn so you don't hit the terra granite. In that case, it'd be worth getting a tailored solution for that airport, IMHO.