This post contains load data way beyond anything in the manuals and may not be safe.
I have no personal experience with 300 grain bullets in the .44 Special. Ross Seyfried has written that he uses 19 grains of H110 behind a 250 cast, and 18 grains behind a 280. The latter load goes about 1100 fps, according to Seyfried. That obviously is well into - and possibly beyond - +P territory. He used them in the mid-frame Bisley Blackhawk and didn't blow it up, apparently.
Brian Pearce, in his great article on the cartridge, listed 15.5 grains of H110 with a 305 grain cast bullet at a bit over 1000 fps, and put it into the 25,000 psi +P category, which should be safe in most modern guns.