I have used 4 Nimh’s with a amc7135 driver without issues. But the 4 Nimh D cells where quite old tired cells so the voltage sag was high. I have read comments of a few other people that have run 4 D Nimh’s with a amc7135 driver without problems. I have also read where several people have had problems with running 4 D Nimh’s. This could be that the batteries they where using did not have a lot of voltage sag, so the amc7135’s had a much greater heat load to get rid of. With 4 D Nimhs it may depend on if the cells are new and how well they handle a 2.8 amp load as to whether they will work or not. Most quality Nimh D cells are not going to have a lot of voltage sag at 2.8 amps and may not work without heat issues. With 3 Nimh’s the issue doesn’t exist as far as I know (never heard of any problems) and should work fine.
4 D alkaline cells I have never tried. 3 D alkaline cells will work fine but at a reduced current level. The alkaline cells cant push more than about 2 amps out because of the internal resistance even if DD. There just not made to push heavy currents. 4 D alkaline cells may work for this reason but I have never tried it. Maybe something you will have to try for yourself. I would be interested in the results if you do.
As for your sst-90 build you might look into a MT-G2 with a couple of li-ions and maybe find a suitable driver here. I would at least weigh the options.