The additional info helped with the following suggestions.
It is not a self-priming pump, in fact it has little tolerance for air on the inlet side. The valve tree that used to be on top of the pump casing was most likely for priming. A couple valves for venting air and supplying water for priming would make sense. Maybe it should come back.
The 1.5 inch nozzle does make the bends on the 5 inch outlet pipe a non-factor. Once the line is filled, the back pressure would limit the pump to at most 580 gpm at 75psi. Numbers from the Elkhart Brass-GPM flow guide-smooth bore.
Having a feed tank with some elevation on the pump prevents vapor-locking in case of cavitation. It would be tough to pull that much through a 2 inch inlet hose without developing cavitation. Lifting from the pond is pretty much out of the question.
A 3 inch inlet hose is better and might be big enough to lift from the pond. It should take about 3 psi for a vertical lift of about 6.9 ft from the pond to pump.
The 5 inch should be even better. This may seem counter-intuitive.
Compare a 5 gallon pail and a stock tank filled to the same depth. The psi the water exerts on the bottom of each container is the same. If you convert the pail and tank into pipes, the pressure to support that height of water stays the same. The fraction of the water that is slowed by contact with the unmoving walls of the pipe, decreases as diameter increases. So a bigger pipe is better, balanced by cost.
The flexible inlet and outlet hoses could be swapped. The smaller hose feeding into the 5 inch pipe doesn't hurt anything.
A 1-3/16ths nozzle would allow about 362 gpm at 75 psi. The tank and feed pump combo would last longer. This would be the simplest change. The pond should be more of an option with a 3 inch inlet hose.
The transition from the small feed hose to the pump inlet is rather abrupt. The large diameter section of conversion fitting should be at least 3 ft long. It would need to be supported though to take any stress off that flange. Great repair job on sticking it all back together by the way.
Larson's Steam Powered Pump- WMSTR
The spout seems to pulse even though there is a lot of water in that outlet pipe, around a 120 gallons. Given the volume and distance from the pump to the nozzle, I'd think it would be more smooth. That's what makes me think there is cavitation going on. Did you ever put a pressure gauge on the outlet pipe? Too bad you can't hook up to the big blue tank for a comparison run.
Here is a site that can be used to test various pumping arrangements;
Hope there is something worthwhile in this jumble of thoughts.