Proper Distributor for HEI Conversion
Up and down play is normal. If you are going to run that blue ford ignition coil it has a male end on it and the distributor you pictured has female ends on it. Not sure if you have an ignition coil wire with one female and one male end. I believe your current stock setup also has a ballast running to your coil which you should bypass to get maximum volts to your new coil (if your new coil doesn't require a ballast resistor if it's a low resistance e-coil which it appears to be).
Are you using the bracket that bolts the HEI module to the bottom of your distributor (
Mopar HEI Conversion)? Make sure you use the thermal paste that should have come with your new HEI module to mount it.