The situation of a black hole is different because all the mass is (*) concentrated at the centre. So there would be no decrease in gravity as you approach the centre.
Time dilation is due to gravitational potential, not gravitational force, so it would increase steadily as you approach the centre of the Earth.
A couple of other points...
The linear decrease of gravity inside the Earth is an idealisation assuming the density is the same everywhere. If you take the density of material into account, the gravity increases slightly first and then decreases.
Also, if there were a hollow in the centre then the gravity would drop to zero as soon as you enter the hollow. In fact, if the total mass of the Earth were concentrated in a thin shell (where the surface of the Earth is) then there would no gravity as soon as you get inside the shell. (But outside, it would make no difference.)