The final version of the fatman can go up to 2.2A max. So, the emitter current could get somewhere in the neighborhood of 510mA. To get this number, I assumed 90% efficiency, 3.6V battery voltage, and Vf of 3.5V. A safer region would be around 460mA (2A input current). With this, total power dissipated by the circuit is around 0.1*2*3.6=0.72 Watts (assumes 90% efficiency). This isn't a lot of power, but it is in the range where heat dissipation is a concern. Even with the fatman, it is advisable to provide a thermal path for the back of the PCB. This is the problem I keep coming back to. And it makes me wonder how the Acorn handles it - either Milkyspit provides a thermal path for the driver or it just doesn't dissipate that much heat because the max input current is 1.5A rather than the output.
I think the Acorn actually can be configured for single stage, but the problem, as you said, is availability.
And as for the 2.7V in requirement, you don't want to discharge Li-ion cells that low - including the IMR cells. You would get the full capacity out of them.
I think the fatman and the shark can do about the same thing here, but the issue with either of them is still heat sinking the board to keep it cool. If you can work that out then you are good to go.