The flange needs to be screwed down to the floor. If it isn't when you tightening the bolts you're pulling the flange up instead of pulling the toilet down.
Are you sure there is a foot valve in the shallow well as there is no reason for it. You have a check valve at the pump. My guess is the check valve is your problem.
That is a poured lead joint. Drill more holes close together so you can pick out the lead with a screw driver. Under the lead is oakum a rope like material that can also be picked out freeing the base from the steel pipe.