XP-S oil is purchased as either mineral or synthetic. The S after the hyphen does not mean it's synthectic. These engines then, were meant to use a non-synthetic oil. The XP-S mineral has a base oil with additives that protect the engine through it's lifetime. The manual also states that if you don't have access to this oil, that you can use an oil of another brand with the same characteristics. Below is a paragraph, directly out of the operaters guide for the 1997 SPX pertaining to lubrication.
Never use 4-cycle petroleum or synthetic motor oil and never mix
these with outboard motor oil. Do not use NMMA TC-W, TC-W2
or TC-W3 outboard motor oils or other ashless type 2-cycle oil.
Avoid mixing different brands of API TC oil as resulting chemical
reaction may cause severe engine damage.
That said and with the oil that your motor has been using, I think I'd drain all that oil and go to Walmart, buy a gallon of the Quick Silver mineral or synthetic blend oil that fits the details of the paragraph above. Quick Silver has several oils so make sure you get the correct one. Read the back of the bottle, it will list that it fits Seadoo's requirements.
Myself, I use the "Full Synthetic" Quick Silver oil because thats what the previous owner used. According to my spark plugs, they like the oil.
To change out the oil, you'll need a vacuum pump to remove the oil from the tank and rotary chamber. You can disconnect the hose going to the top of the tank, which is the vent line from the rotary.
When the oil is out, you can take a rag, hold it at your injection pump and break that fitting there, drain the little bit in the line and put it back on. The top of the oil injection pump, you'll see a bleed screw. Remove it and bleed the oil till you have no air bubbles.