Just jumping in on the discussion of higher current with more open flow of a centrifugal pump. I always looked at it as to how much WORK was being done. Higher volume rate = more work - - more work = higher current. Isn't that how the fellow first defined horsepower? Have a horse lift a given load a given distance in a given time?
I have a fair amount of experience designing controls for high pressure hydraulic systems and troubleshooting them as well, from an EE's perspective. For someone who claims to be learning about this stuff you certainly are doing an excellent job troubleshooting!
While I completely agree with everything Max said about impeller pumps, you do not have an impeller pump. You have a CAT pump (see attached pdf). Cat Pumps are triplex (beats me if I know what that means!), positive displacement, reciprocating pumps. The more the outlet is blocked the harder the pump works (and the slower it will turn) and the motor will draw more current . When there is no flow at the outlet the motor will stall. However, these types of pumps use what is typically called an unloader valve to prevent that (some people call them relief valves but some mechanical engineers may disagree with that terminology). Unloader valves can be actuated in a variety of ways but ultimately allow the pumped fluid at the outlet to flow back to the inlet side of the system thus preventing the system from "stalling".
I found a pdf that looks like it might be for your system or one very similar to it. The parts diagram looks very much like your photo. I didn't see anything specifically called an "unloader valve" but it might be incorporated into the pump itself or is possibly one of the Asco valves. Any chance what you made a mistake on had something to do with the unloader circuit? "Circuit" here could be hydraulic, electrical, or mechanical in nature.
I didn't see a hydraulic schematic in the pdf, maybe I missed it. It sounds like you're the "go to" guy when things go wrong, a hydraulic schematic can be pretty handy to have when troubleshooting. You might try to weasel one out of the manufacturer.