Before going any further, do a compression test first. You can rent one from auto parts store for minimum cost. Make sure you do all cylinders for comparison purposes. If the compression is good, it is most likely the intrusion is in the exhaust gasket. If the compression is bad then the intrusion is most likely in the head gasket.
After many years of work on these motors, you will be more than happy if the intrusion is due to a torn head gasket than an exhaust gasket. Unlike 4-cycle engine which has multiple parts mounted on the cylinder head, i.e. cam shaft, timing gear, valves, etc, on these 2 cycle motor there's barely none except maybe for the spark plugs and T-stat.
On the otherhand, if the leak is on the exhaust plate or gasket it's not about the parts mounted on it but the pain and hard work to remove the bolts that are exposed to heat and water. Yup, the bolts are heavily corroded and most breaks easily making removing the left over broken stud a real PITA to work on.