generally you can find an alternative sealed battery to go in those battery packs as you have already found, champion battery prices are totally rediculous, going with the alternative should work fine as long as the battery you are installing is the same rating as the one you are removing.
as for the yale , if they are lead acid (wet) batteries they do need to be checked.
changing battery packs from one unit to the other should not have any bearing on the motor issue unless you have bad batteries , that can cause low voltage, high amp draws in the motor and will burn one up.
check the motor in the yale real good and make sure the armature is not burned , most likely it is and the whole motor will have to be replaced, repairing the armature (if possible) generally does not last.
Also load test all the batteries in the yale battery pack and make sure you do not have any bad ones, replace any that are.
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