Variable speed blowers work well in single, and 2 story houses.
Closing the dampers as you are, may be the cause of your heat exchanger problems, if it indeed does have holes or cracks in it.
Since closing those dampers, decreases the amount of air over the heat exchanger.
Do not close the dampers, adjust them to lower air flow, but not stop it.
If you do that with a variable speed blower, it will make the blower work harder. Use more electric, and could be harmfull to the motor.
Depending on type of heat exchanger cell you have, failing a water test, means nothing.
A visual inspection should be done.
Before you just replace that furnace.
Have a load calc done, to determine what size equipment you need.
A proper sized furnace, will have longer run times then an oversized one. And give you a more even heat in the house.
Same with A/C.