I would rather turn them back before acceleration, to keep them in an area I am very positive of the obstacles.
if one is not very positive about the obstacle profile, one has NO business scheduling the escape path over that area. The problem with accelerating first is that the distance covered (take the DC9 as a nasty example) can be VERY significant ... turning back in the second segment, where feasible, saves a lot of ops eng hard work.
As far as TORA, TODA, ASDA, and gradient are concerned the result will be more conservative than actual achieved performance.
Perhaps. However, unless that protocol is prescribed explicitly in the AFM .. I would be getting OEM concurrence with the presumption of conservatism for contaminated fluids where mean fluid density becomes a driving factor. Likewise I have a concern with tapeline heights as you have identified in your subsequent comments.
In the sim, I reach acceleration altitude (1,500) before the 5 miles. What do I do, then?
I have no familiarity with the aerodrome so I am speaking generically.
(a) if you are AEO, keep climbing until you complete the turn - the only concern should be engine thrust time limits and they ought not to be a problem
(b) if you are OEI, and the failure was near V1, go back to your ops eng and suggest that they redo the sums
(c) if you are OEI, and the failure was well post V1, keep climbing and commence the third segment after the turn. If that puts you past the engine limit in the sim, you might run the concern past your ops eng folk for resolution and review of the procedure.
From the sound of your description, the company procedure is not well thought out or described - my suggestion is that the ops eng folk should revisit it to sort out the problems.