I wasn't actually thinking that this was the complete answer,...

I wasn't actually thinking that this was the complete answer, but there are several things they could borrow from it.

The fact that it can be floated into position using three tugs before it is submerged is a plus.

The rock mat can be lowered onto any type of bottom, even if uneven. Levelling and grouting can be controlled from the surface to ensure it remains evenly seated.

I don't imagine it would be too difficult to pre fit the female component of the stab connector into the rock mat.

Using the rock mat as the centre piece, other methods of anchoring could then be added to give it extra holding power. Perhaps drilling on the skew below the structure with several embedded anchors attached may be the answer, or suction caissons as you suggested.

Obviously it would not be economic to have to pump thousands of tonnes of concrete, but if the additional anchoring was effective, a smaller version of the rock mat might be sufficient.