Since the sleeve is the limiting factor I wonder if it is an airflow problem. If you are testing on a bench, can you test with the sleeve only partially installed at different levels and see if it works? Maybe once you find the point that it stops working the problem may be more obvious.
Does the furnace work inside the sleeve, but with the sail switch unplugged and the wires jumpered together? Don't leave it like this, but it is a test I would probably try.
Also in the link I provided above there is a Suburban Technical Information link (fifth one down in the Furnace Service Manuals section) that describes each part of the system. In that manual they describe the 10 most common failures of the furnace.
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2001 Suburban 4x4. 6.0L, 4.10 3/4 ton **** 2005 Jayco Jay Flight 27BH **** 1986 Coleman Columbia Popup