Remove poor, shoddy tarmac and turf?

[Ouch77]

Some bright spark in years past (70's I reckon, given what other detritus I've dug up) had decided to lay some tarmac type stuff in my back garden, in a strip adjoining the lawn.

My desired outcome is to extend the lawn over this area (about 1x7m).

It's a fairly undefined patch of tarmac, kinda blended into the mud over the years, approx 4-5inch thick, and brittle as hell. It's been laid directly onto soil/clay (no sub-base layer or anything), with the odd bit of waste building material chucked in for good measure (halfbrick and the odd breeze-block). I'm pulling it up with a mattock, in lumps from fist size to half metre square. The problem is that it's leaving a lot of gravelly remains which then end up getting mixed into the clay beneath.

The lawn itself is okay, but a tad lumpy, (I dug a dispersal land-drain into it last year), ragged around the edges, and not quite the level I need it at. I'm thinking the best approach would be to start again with fresh turf, as this will hopefully give an even appearance across the whole area, and be usable sooner, as the good weather is (supposedly) around the corner and I have a young family wanting to play in the garden.

So my strategy is:

1. Remove the big lumps of tarmaccy stuff
2. remove as much of the gravelly remains of ex-tarmaccy stuff - any tips for this?
3. Cut short then nuke the lawn with non-persistent weedkiller.
4. Carefully rotivate (don't want to rip up the land drain) the whole area to allow the remains of the topsoil to be redistributed
5. Add topsoil and some sort of improver if required - again suggestions welcome
6. Rake level, lightly compact/roll
7. Lay new turf.

Can anyone see fault or problems with this? Suggest any improvements or alternative approaches?
Comments and thoughts welcome..