a loud click could be lots of things.  First thing I would do is remove the pump and turn the engine over.   If the click goes away you know it has to do with the pump.  If it continues to click then try and figure out where it is coming from.  Sounds like that can be all kinds of things from major issues to minor ones.  

Thats probably major then.  Could be a valve it could be a broken piston ring.  Take the valve covers off and pull all the spark plugs and turn the engine over by hand see if you can get it to clunk.  As you turn it by hand see if any of the valves look like they are not moving correctly.  See if you can pinpoint which cylinder is clunking.  I would not turn it over with the battery.  At this point that could make things worse.  

Well after I thought about the circumstances leading up to the clunk, I decided that it had to just be the battery.  So against your sound advice, I gambled with a different battery...  Turns out it was just the starter not getting enough juice.  I am surprised how loud a noise the starter made, but it's turning over just fine now.  I've had a fuel supply problem, and after a filter, new hoses, and a new fuel pump, I discovered the rubber hose that connects to the gas tank was crimped.  So all in all a good day working on the Galaxie.