By the Numbers
By your posting I am positive you are a multi engine instructor - who has never done anything but.
Yes a Seneca or Duchess will climb perfectly well, with a couple of POB in most situations around Australia. Where we operate piston charter twins most of the time, they certainly won't.
The key - is to expect the aeroplane not to perform and plan accordingly, then be surprised when it does. It certainly is not a happy day when you are expecting performance, and it does not (a friend of mine was taken recently because of this). Chimbu Chuckles once said something quite profound. He never expects an engine to perform for the duration of a flight, and is pleasantly surprised when it does. I think you should adopt the same attitude, and plan accordingly, then accept the reality of your piston twin performance.
The 1% climb gradient to 5000 feet needs to be also explained (slowly just for you). If you are grounding 100 knots, that is only a 100 ftpm ROC. Now you could be achieving this, and losing this PLUS MORE, in thermal turbulence and down-droughts. 100 fpm ROC is not something that is going to give you much love. In simple terms it will take you 10 mins to climb 1000 feet. This will also put you 16 miles or so from where you started. Unless you are taking off from a flat island in the middle of the ocean, once you are outside the protection of the circling area you will surely be below the 10/25nm MSA and en-route LSALT.
If you want guaranteed performance, fly something certified to achieve it (under 20.7.1b). Even then, sometimes due to the nature of the beast - you can not necessarily rely on it.
Let's also get this straight, the 1% climb gradient is only required in ISA (along with the other performance requirements) conditions. They are certainly not required to achieve this performance in ISA+ under their certification. As the operating Pilot, you are also not required to ensure they can. You are just required to understand the limitations. If you want to maintain these margins, you will never be able to operate piston twins with more than a couple of POB in ISA+ conditions.
Before you start crapping on about how they should be banned if this is the case, why do you happily fly in singles? A piston twin is basically a single engine aeroplane with the engine divided by two and bolted to the wings. Treat is as such, and you will not have a problem.
As for the accident, this does not appear to be the cause of it, so lets put this one to bed.
Next.