Best material to level concrete porch from 2 3/4" to zero?
 

Problem:

Old concrete stairs leading to concrete entry porch (5' x 8') have been
rebuilt out of wood. New stairs are level. Porch is out of level by
about 2 3/4" over 5 feet. Riser height of new stairs is 7 7/8". Top
riser is old concrete resulting in a wedge that is 7 7/8" at the house
(stairs run alongside the entry wall) and about 5" at the other end,
resulting in a trip hazard.

Top wooden tread is wider by half an inch, 13", than the lower treads
which are 12 1/2" wide. Top conc riser is plumb. I need to place a form
board at an angle to achieve a nosing. Form board will be spaced 1/2"
from the conc riser at the bottom where it intersects the top wooden
tread and will lean away from the conc riser to achieve the nosing.

Porch is being stripped of paint and will be power washed and scuffed
with a carborundum grinder, and concrete bonding adhesive or a mixture
of Acryl 60, sand and cement will be used to get to a good surface for
adhesion of new material. Wire mesh and #3 rebar will be used where
practical, especially in the new concrete nosing.

Question:

What mix should I use to have the best chance of getting out of this in
one piece?

A hod carrier friend who mixes for plasterers suggested that I use conc
with pea gravel where deep enough, then sand, cement and 1/8" agg (he
suggested aquarium gravel) where the depth gets down to less than an
inch, and then cement and fine sand where it feathers to zero. We didn't
discuss what to use between the new form board and the old concrete
riser but I would guess the sand, cement and 1/8" agg would be
appropriate, perhaps with some admixture like Acryl 60, which would
probably be a good idea to use everywhere.

I'm considering using the first two mixes and only pouring to a depth of
1/2", where I will use a small form to create a roundover edge to the
conc and then come back after this has set up and use another
appropriate material to feather to zero the remaining 12 to 16 inches. I
would rather do it all at once, though. If I'm organized about it, with
the the right materials on hand, and enough buckets and troughs to mix
the different mixes, I feel I should be able to knock it out in one go.

The big concern is where it gets thin, less than 1/2 inch. Is there
anything more better than sand, cement and Acryl 60?

tnx,
Jack