ASDA not ASDR should always longer than EDR (As I understood Engine inop go distance required stated here is the EDR)
TODA is fixed for the runway and is applicable both for the AEO and OEI TODR calculations. Which of these is limiting will depend on the aircraft, runway and ambient conditions. TODA will include any clearway up to the maximum declared by the airport authority and usable for the aircraft. What ASDA is declared will, likewise, depend on the runway design and the airport authority's declaration. Whether TODA is less, equal to, or more than ASDA is not fixed but specific to any particular runway. Although it's a question which I don't think I've ever fussed over too much, I suspect that, for most cases, ASDA will be less than TODA. Your statement is not quite correct, I fear.
As for the 3051 m from the software, I am sorry but I cannot trust it until I get a clear explanation.
Now, you might have some difficulty doing that. Suggest you run it via your CP, who should then run it by your ops eng folk, who, if they can't provide an answer, should run it back via the OEM .. which might, perhaps, give them an answer.
if the objective is to become airborne in the shortest possible distance you don't want to gain _any_ additional speed after vr,
However, the objective is not to do that. Rather the objective is to replicate, as closely as the pilot is able, what the AFM says is the required takeoff technique. I really think that you should revisit the certification logic lacking in your statement.
I was just not immediately seeing how an AEO go-distance could sensibly be longer than a OEI go-distance, v1/vr being identical explains it according to the above.
Not so. For that case, the OEI distance would be greater than the raw AEO distance due to the OEI thrust rundown. However, the AFM-scheduled AEO distance very likely will be greater due to the AEO TOD factor incorporated in the scheduled numbers. This often is the case where OEI performance is reasonble - think lower weights, lower pressure heights and temperatures.
The first set suggest that min v1 is used...
I wouldn't have thought so. The OEI/AEO TODR split doesn't appear to support that view.