A certain amount of unburnt oil is discharged on a two stroke engine BUT it is not ingested into the cooling system, rather it is simply released via the exhaust system.
You say that the engine wouldn't run at all unless the choke was engaged, then go on to say that there seems to be an issue with the spark..... Start with the proper trouble shooting procedure or you'll be second guessing until doom's day (as follows).
The spark plugs should be Champion QL77JC4 plugs gapped at either .040 or .030, your gap choice as one or the other might provide improved performance at either idle or full throttle... varies from engine to engine.
With all of the spark plugs removed, check the compression. What are the psi readings of the individual cylinders?
With the spark plugs still removed, rig a spark tester whereas you can set a gap of 7/16" for the spark to jump that should have a wide blue lightning like flame... a real SNAP. What kind of spark do you have? NO tester?... Build the following.
(Spark Tester - Home Made)
(J. Reeves)
You can use a medium size philips screwdriver (#2 I believe) inserted into the spark plug boot spring connector, then hold the screwdriver shank approximately 7/16" away from the block to check the spark or build the following:
A spark tester can be made with a piece of 1x4 or 1x6, drive a few finishing nails through it, then bend the pointed ends at a right angle. You can then adjust the gap by simply twisting the nail(s). Solder a spark plug wire to one which you can connect to the spark plug boots, and a ground wire of some kind to the other to connect to the powerhead somewhere. Use small alligator clips on the other end of the wires to connect to ground and to the spark plug connector that exists inside of the rubber plug boot.
Using the above, one could easily build a spark tester whereas they could connect 2, 4, 6, or 8 cylinders all at one time. The ground nail being straight up, the others being bent, aimed at the ground nail. A typical 4 cylinder tester follows:
..........X1..........X2
.................X..(grd)
..........X3..........X4
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Now, if you have proper spark and compression, that leaves the fuel section. In cleaning the carburetors, did you manually clean the four brass high speed jets that are located horizontally in the bottom center portion of the float chambers... in back of those four drain screws/bolts? If not, do so as cleaning solvent just doesn't do that job properly, and fuel must flow freely thru those jets before gaining access to any other fuel passageway.