As you back out the bolts evenly, you will notice the pressure on the pump from the pushrod location. Rotating the prop can increase or decrease the pressure. Less pressure makes removing the pump easier. Back out the far bolt first. Switching when you can't go any farther.
Make a 6 inch dia. loop of string. Regular string has enough drag that it will hold the rod in place better than wire. With the rod in the fully up position, work the string up the rod so it loops around the rod. Not a sling. With the rod in the up position hook the loop of string with a bungie and hook the other end to something near that will place pressure on the string.
Use Permatex #2 on both sides of the gasket AND the threads of the bolts..... The case is drilled and threaded through, so it can leak!
As you install the new pump, start with the far bolt and move the pump in evenly. As you go, you can push on the pump to confirm you are on the rod. It should spring back. When there is still a small gap between the gasket and the case (1/8") disconnect the bungie cut and pull the string out. Tighten the bolts and safety them.
But first.... when you have the two pumps side by side, remove the fittings from the old and clock them the same on the new pump.