Well, when it goes up with oil that means your rings aren't sealing properly but before I would trash it since you said you had lots of carbon on it, there's a high degree of likelihood the rings are just coked up in the Piston lands.
This was the problem with all the old original Saturn car engines and made them use oil and lots of it.
The best fix for this or at least the easiest is to get the engine tilted up a little bit or I guess it's called back so the spark plugs are kind of up in the air. Straight up is better but 45° will work.
A lot of people use seafoam but I prefer to use berryman's B12 and you get a funnel and you place the cylinders about Midway down or so and you pour at least two inches of the cleaner into the cylinder through the spark plug hole and a funnel or a tube.
Let it sit there for several hours and then if it all disappears and goes into the crankcase fill it up again.
For a twin like this I would use the whole 12 oz can of berryman's B12 or seafoam.
Then after it soaked for several hours I like to grab the pulley underneath the engine and rock it back and forth about 3/4 of an inch each direction.
Just enough for the Pistons to go up and down but not move enough to force any of the liquid out..
I want to rock it back and forth quickly and 30 or 40 times so it helps those rings get pushed to the top and then the bottom and the respective lands in the pistons.
Then, get you some towels and point it in a safe direction and get it all flat again and crank the engine over but be careful because it will blow any of the liquid that's still in there across the room.
Then put the plugs back in and start it up.
Once you know it runs, change the oil and only use one of two oils.
Mobile 1 European 5W-40 or rotella t6 5w40.
These are both fully synthetic oils that I would actually recommend the rotella because it has a higher detergency.
Put the old level all the way to the full mark if not an eighth of an inch above and run the engine for normal use.
This has an absolute wonders to some engines that have smoking and ring problems and especially those Saturn cars too.
It gets noticeably better quicker but it will continue to improve even a lot more as the oil continues to work and as soon as it starts to look dirty, with any of the carbon getting it darker than a nice clear look, change it again
