The short answer is running the engine at rated or max engine RPM will give you slightly more lifting capacity.
Your pump is positive displacement so each revolution of the pump generates the same volume. The faster the pump turns, the more flow it generates. The more flow, the faster a cylinder will move. Pressure equates to how much force it takes to move a cylinder. The more load on the cylinder the higher the pressure. The relief valve limits the maximum pressure and therefore the maximum load the cylinder can move. The relief pressure is mostly independent of the flow. Two good points raised here by others (SPYDERLK & MHarryE), internal leakage takes some of the pumps output and the poppet relief valves have some non-linearity with flow and oil temperature. High flow and cooler oil will give slightly higher relief pressures. To get the maximum lift capacity, run the engine at rate speed and do the heavy lifting before the oil gets hot.
If suprnova is correct that your lifting capacity is 1058 lbs at 24 inches sand you cannot lift 883 lbs, then you may have other issues. But first, is the center of the 883 lbs within 24 inches? (Pictures are nice) If the center of mass of your attachment is beyond the 24 inches, then you may be exceeding the lift capacity.
Are there multiple holes for the lift rods to connect to the hitch arms? If there are, you may need to move them further from the tractor. That will reduce lift height range, but increase lift capacity.
Your signature says you have a backhoe. Do you switch a valve or connect a hose loop when the back hoe is off? Double check that you have that correct and quick disconnects are fully seated.
Your relief pressure could be low. You would need a gage and a fitting to connect the gage to your backhoe supply quick disconnect or one of the FEL quick disconnects. If it is low, you will need to get the relief valve adjusted.
You could have an internal leak in your 3 point cylinder or valve. Will it hold up a load with the tractor off? Note that the 3 point speed control only affects lowering speed and has nothing to do with raising or lift capacity.