Understood.
Given that you need to drive the 8 rows independantly to make them all zero, why not just note the number you write to the top 8282 and convert it to 4 bits in software. It seems overkill to use two ICs just to convert the number you start with into a different radix.
I can't see any electrical problem that would cause damage. It isn't clear what the components on the top and right side of the matrix are but I assume they are pull-up resistors, you don't need them on the rows because the top 8282 is always driving them. It would be advisable to add resistors (about 100 Ohms) in series with the row signals to the matrix just in case more than one key is pressed simultaneously, the resistor would limit the current that might flow between high and low signals on the outputs of the top 8282.
Brian.