I think you just have provided the first honestly relevant answer yourself.
If the numbers are done right, the fork point EOSID vs. SID creates two safe routings however there's no transiting from one to the other. The assumption done at the calculation phase is that pilot will choose only one. Looking at the paperwork, you may find the splay area of EOSID is as narrow as 850 m on each side. Not that the edges are made of granite, but the protection is assured only within.
Should this ever actually happen, there will be many options that are equivalently safe to pursue as following the EO-SID. Standing by his commitment of following the most conservative, least risky option that allows for the greatest margins, the PIC will decide accordingly.
What we are discussing here is a mere paper exercise, which has paper-worth answers. Don't get me wrong, they are both valid and required in the pre-flight stage, must be even submitted to gain ops approval. But whoever trains for this better make sure the students will understand well what the limited scope for this exercise really is.
Here's a not-so-curved ball.
Departing LFPG (4 parallel runways), the EO-SID have you cross the departures of the other two runways. Call mayday and advise the turn, let the ATC care about the rest - they say.
Enter your scenario (using A319 loaded for 1 hr sector - she climbs with 5,5 % on one engine at MCT and the other one dead) You only need to retard until 67 N1 where the sore engine starts behaving again. It's a nice autumn VMC...
Is joining the EFP the necessary safest option?
Even the language is funny on the wrong side: EO-SID - there's nothing standard about it ... I liked the EFP terminology better.
Some companies have EFPs for absolutely all runways, until 25 NM out and then it ends.
Some insist there is a close end to each of them (holding).
Some use SID's and claim they did the research unless there is EFP
Some say climb straight ahead, we did the research otherwise there would be an EFP.
Some provide the decision point and do the research for SID routing
Some provide the decision point but claim thereafter it's "doable"
Some factor airspace constraints into EFPs, some don't ...
Clear as mud, uh? A 100% proof solution is extremely hard to find and costly to develop. Whereas the real risk and probabilities pose a threat for which a perfect answer is not actually required. One of the many aspects of aviation where getting it absolutely right will make you go insane, yet have a negligible effect for a real-life occurrence should the day ever come.
Training is a finite-resource activity, not only for money and time but also how much will the students
correctly remember a year or two later. The subject and amount of detail need to be carefully considered.