Detect black/white at 150 mm
Use two different sets of markings on your disk with two different detectors, one aimed at each set.

The first set is simply a regular pattern of light and dark bands, which give you the rotational speed of the disc by measuring the frequency of the signal from the detector. Put this around the outside of the disc for maximum accuracy and resolution.

Then, closer to the centre, put a pattern of pairs of bands, one of which is, say, twice the width of the other, with a gap between the pairs that is larger than the whole pair. The detector aimed at this pattern will return a shorter pulse followed a longer one if the disc rotates in one direction and the opposite in the other.

With a 400mm disc to play with you ought to be able to get the different detectors far enough apart with relatively simple masking.

With enough processing capability, you may even be able to put the bands closer together and use a well focussed single sensor, then extract both patterns from the signal it picks up.

You may even be able to combine the patterns in this case such that you have maybe ten even bands then a thin one and a thick one. The frequency will be unchanged but a periodic variation will give you the direction. Vehicle engine systems use techniques like this to provide timing and location of Top Dead Centre (though they obviously don't worry about direction).