I ave also been searching for higher output supplies for charging. I have found some that are fairly easy to modify and bought several so I could drive shipping down and resell them to other modelers.
Note that the larger one does 84A at 240V
I have also been frustrated at the lack of available documentation.
RE the wires soldered to the outputs - As you can see from my pics the IBM X235 power supply has the same output plug as on the HP here. I first tinned my leads then flatten them with pliers. Then I push them into the connector on the supply and solder them in. Works great for over a year. You should also have some sort of strain relief as I see you ave done to prevent the solder joint from seeing and physical load.
Yes I'd like to know how you figured out how to get the supply to turn on.