Coffered timber ceiling for a 22 sq m home study

I am finishing a study in a private house and want a proper coffered ceiling there instead of the flat painted plasterboard that is up now. The room is 22 square metres, roughly 5.4 by 4.1 metres, with a clear height of 2.95 metres from the finished floor to the slab. The slab itself is the main problem: I measured it with a laser level and there is a drop of about 35 mm across the long side, with a local hump near the window. So the first job is a levelled service frame, and only then the visible woodwork. I do not want the grid to follow the crooked slab, I want it dead flat and square to the walls.

What I have in mind is a grid of five by four cells, which gives cells close to a square of roughly 1000 by 980 mm. Beam face around 140 mm wide, drop below the finished plane around 110 mm, boxed rather than solid, with a mitred profile running along the bottom edge of every beam and a small inner profile framing each recessed panel. The panels themselves can be painted MDF, since they are flat surfaces and will be seen from below in soft light, but every visible beam face, the profiles and the wall cornice must be solid wood. My preference is oak or ash, tinted to a medium warm brown with a matt finish, no gloss. I will want two or three tinted samples on the actual species before you spray the whole lot.

Each cell gets one recessed spotlight in the centre, so twenty fittings in total, plus a shadow gap detail where the perimeter beam meets the wall cornice. Wiring is already pulled into the slab, but the final positions must be set from your grid, not the other way round, so we agree the layout on site before anything is cut. Please quote for measuring, shop drawings, making, delivery, installation, filling, sanding and finishing on site. Tell me what you need from me and how long the whole job takes from the first measurement to a clean room.