Ports PA, PC & PL look to be 8 bit wide ports on the Mega that are not doubled up or part of standard Arduino pins so maybe you could use them to connect your 19 bit address.
The direct port manipulation info here does not cover the Mega but the principle is the same.
Once you have setup all the port pins for input using the DDR registers
The reading code can be simplified/compacted but as it is it shows how you read Port A and rotate the bits up by 8 then read port C and rotate and finally read port L.
Address will contain the 19 bit address from the ports in the form AAACCCCCCCCLLLLLLLL