I don't think you will be able to crank the motor over to purge the old oil, and you won't be able to get rid of all of the oil oil either, just some of it. I think you need to find a way to reach the oil pump bleed screw, study the drawings carefully so you'll know where it is.
The reason you need to bleed the oil pump is to remove any air bubbles in the supply line, air will interfere with the pumping action, the pump doesn't work well if there's air in the rotors.
As for the oil in the lines, you can pull them off and blow them out with a few psi of air, the DI has an oil return system from the air compressor back to the oil tank so you could temporarily reroute and catch that return oil into a temporary catch bottle as the engine runs for a few hours(or couple days) in the water so your XPS isn't contaminated by residual of old oil. This is what I'd concentrate on as opposed to attempting to purge out the old oil from all the lines.
So in summary, this is what I'd do:
1) Drain out old oil from oil tank, remove tank and wash it out, blow dry with air. On mine (carbed motor) I simply left the tank installed and poured XPS through it, wasted about a quart.
2) Replace oil strainer filter
3) Reconnect supply line to oil pump and purge air through bleed screw (I was very careful not to get air bubbles in the supply lines, so this was unnecessary)
4) Rig up a return catch can from the air pump.
5) Start ski and hold oil pump lever 1/2 of full travel position to allow high XPS-II flow rate, engine should smoke noticeably. Or you could adjust the oil cable rich(tighter) instead of trying to hold the pump lever while the engine runs(b/c it's really tough to get to pump while engine is running!), you should check the cable adjustment and realign the marks anyway, once you've finished working on the injection system. You'll need a mirror and flashlight to see what you're doing, I needed glasses too b/c the oil pump lever alignment marks are small and hard to see!
The 947 motor receives almost no oil (~ZERO) at normal idle speed, you'ld be hard pressed to measure the flow, so holding the pump lever at about 1/2 of it's travel will allow oil to flow and purge remaining air bubbles as the motor idles. Shoot some oil into the throttle body intakes if you're not sure there's enough inside to lube the motor (look for smoky exhaust = enough oil)
As far as sooty black plugs go, I'm thinking soot from excess fuel (ie:leaky fuel injectors spraying fuel into the cylinders and diluting the lube oil), or it could just be from fogging the engine with cosmolene or some other heavy amount of oil, it's hard to know.
I would avoid removing the air injectors, the carbon dams would need replacing if you removed them. Hopefully someone hasn't done this before you.
Mixing of 2-stroke oils can cause congealing, change viscosity too heavy, and stop flow, especially in the oil filter strainer, but if the tank and line is cleaned out up to the oil pump and the weather is warm, the two oils won't exist together for long, so I think the best way is by just catching the return oil from the air pump so it doesn't contaminate the XPS tank.
My carbed boat had the wrong oil in it when I brought it home but it ran fine and the plugs weren't sooted, but I'm pretty sure it was TCW-3 outboard engine oil, not some kind of indestructible cosmoline or something, so soot on plugs doesn't add up in my mind unless someone oiled the heck out of it, in which case it will take some time to burn it all out.
At some point the rubber oil lines from the oil pump to the bottom of the intake manifold and air pump oil supply should be changed b/c they do rot over time and if they crack or leak the motor could be starved of oil. The rubber material is Tygon F-4040-A, 3/32 id
I don't think you'll be able to completely purge the oil trapped in the air pump crankcase, it'll take a bit of time for that oil to work it's way out of there.
Hopefully some of these ideas help.