Accupower D NiMH cells can hold over 1.2V at 5A draw. At 2.8A draw, you should be close to 1.25V per cell, or a Vbatt of about 3.75V for a 3D Mag.
The main issue is reducing parasitic resistance in your Mag so that at 2.8A, you don't suffer excessive voltage drop.
Certainly, using 4xNiMH would give you plenty of voltage headroom, with lower but perhaps (barely) acceptable driver efficiency. The NiMH battery stick that you linked, however, is too much. It uses 5x1/2D. Five NiMH cells are going to start at say 7.5V, and run at about 6V quasi steady state. If the high initial voltage doesn't kill the driver, the high steady state voltage will result in poor driver efficiency and a lot of heat generation.
The ShiningBeam driver is the usual AMC7135-based driver and those AMC chips have a max input voltage rating of 7V and a recommended max of 6V. Any voltage over Vload is just wasted as heat. Thus, the goal is to provide enough Vbatt to satisfy Vload (i.e., Vf) plus some overhead to address parasitic losses and to stay in full regulation for most of the run time.
When you use 3xNiMH, you want a low Vf LED to maximize the voltage overhead that you have available.
If you run an 2.8A AMC-based driver at 6V steady state driving a P7 having a Vf of say 3.3V at 2.8A drive, your driver efficiency is going to be essentially 3.3/6, or about 55%. That's not very good. You are generating about 7.5W of waste heat.
The closest match is 3xNiMH when using an AMC-based driver to run a P7 at 2.8A. That is probably the preferred battery configuration for a D Mag P7/AMC7135 mod, with the caveat at the top of my post that you reduce sources parasitic resistance/voltage drop.