Condensation at roof, down outside of furnace/water heater vent. What is happening?
What is happening, you have diagnosed correctly, in my opinion. 

How to fix it, not so well. 

The standard projection for chimneys from roofs is "2 feet above any part of the roof within 10 feet", or in this case, 2 feet above the ridge. You need to extend the "actual chimney" to meet this (IMHO) not cut down the sleeve to meet the "too short chimney." The chimney should extend higher than the "sleeve" and have a rain collar to divert any water coming down the chimney outside the sleeve.