What radius and rotation would be needed to produce 1g consistently from the floor to a height of about 6ft (2m)?
Infinity. Technically there will always be a vertical gradient of artificial gravity. Realistically, people will not care. Even with a radius of 224 m the difference isn't much. The acceleration for anything attached to the structure will be:
This makes the problem simple because the rotation rate (omega) is constant, so the difference between your head and feet is r1/r2. For a person standing in a 224 m radius structure, that's 2/224 = 0.9%.
For reference, the tidal forces on Earth cause a difference in gravity of 0.00006 % from your head to your toe. Earth has an exceptionally constant gravitational field. If you like, you can calculate the radius needed to produce this degree of consistency. It is about half the radius of the Earth.
A percent difference in acceleration from head to toe shouldn't bother someone too much. The main concerns of discomfort in artificial gravity are dynamic Coriolis (false) forces. These are not static like the effect your mention. The terms depend on velocity, not position, so someone standing still will not feel them (discounting any moving fluid in their body). For normal motion, these are much more significant.
Here are some images of dropping an object in artificial gravity. For the 2 rpm case, there is significant noticeable deflection. But again, due to forces that only occur when something is moving relative to the ground. So you could have 1% difference in gravity due to radial location, but several centimeter displacement from dropping something. The latter will be more noticeable.