short of having a bad new pump....there has to be
something wrong with the eccentric. it may be there physically but, the hole could be chewed up or the bolt is lose, therefore causing it to not be offset & not able to move the pump arm. (you mentioned it had alot of side to side movement, it should not have any)
so....unless there is something clogging the line(s) or the pump is bad, it kind of has to be the eccentric. test the pump as mentioned above & see if it pumps fuel, or you can just put your finger over the intake hole & pump the arm to see if there is suction. if there is, it is most likely a good pump.
a fail proof eccentric test is to feel if it's "offset" with your finger, or something else you can stick in there. due too the mentioned "risk" of damage to your finger try this.... have someone turn the engine over by hand with a socket on the front dampner bolt. (remove the plugs to make it turn easier) that way you can
safely feel if the eccentric is operating properly. it should move in a sort of out of round circular motion. if it doesn't that is the problem. but if you are carefull as i said, you can just have someone lightly bump the key so you can feel it move. unfortunantly that is the only way to verify the eccentric is good....
i hope that's not it but like i said, i just had a car that had the problem & my friend's t/a just did it a week ago. test the pump/eccentric & keep us posted.