DIYbanter - reparing a hearth

I live in a late victorian house. I am in the process of removing the
old fireplace and inserting a firebasket. I have taken out the old
fireplace. The hearth in the fireplace was built up using bricks and
cement. I have removed all this and am left with a hearth at
approximately flush with the floor. The hearth in front was made out
of bricks and cement. I have removed this and underneath is the
original hearth which is also approximately flush with the floor. This
original hearth appears to be made out of a lime, sand, cement mix, is
about 3-4 inches thick and rests on the joists(?). It is old and
crumbling a bit around the edges.

My plan is to put a new layer of sand, lime, cement mix on both
hearths, about 3-4 inches in depth. This would then give a single
raised hearth. I would then put slate on top. Does that sound
sensible? Or should I remove the old hearth and start from scratch?