Sorry so what you're saying is if we did this experiment;
I had a perfect ball of lead encased in say, a golf ball like capsule, then an exact same golf ball like capsule with no lead inside, you drop them from the same height at the same time. they should land at the same time because the air resistance would be the same? It wouldn't happen that way... the capsule with the lead inside it would drop faster and hit the ground before the empty capsule.
So the the proven theory of gravity is already more plausible than your 'theory' of air resistance and constant acceleration in this case. So how do you prove otherwise?
If no air resistance is present, the rate of descent depends only on how far the object has fallen, no matter how heavy the object is. This means that two objects will reach the ground at the same time if they are dropped simultaneously from the same height. This statement follows from the law of conservation of energy and has been demonstrated experimentally by dropping a feather and a lead ball in an airless tube.
When air resistance plays a role, the shape of the object becomes important. In air, a feather and a ball do not fall at the same rate. In the case of a pen and a bowling ball air resistance is small compared to the force a gravity that pulls them to the ground. Therefore, if you drop a pen and a bowling ball you could probably not tell which of the two reached the ground first unless you dropped them from a very very high tower.
Both of these will ALSO be true within the frame of a constantly accelerating Earth due to Relativity. Your answer of 'the lead filled will hit first' while technically correct, will need relatively specific circumstances to be detectable AND will be true under the common UA model as well.
What Pete has said, is it's possible to take two objects with the same mass/weight, and in an environment with air have them fall at different rates. Consider two pieces of paper. Same mass. One left flat, the other crumpled into a ball. Do you propose if I drop them both from a height they will both hit the ground at the same time? I should hope not, for you will be very wrong if done in an environment with atmosphere and no 'guides' for the flat sheet of paper. Parachutes work on the same principle.