Johno, replacing the rings will not improve the piston slap problem. The piston skirt (i.e. just above the bottom edge of the piston) should have a maximum permissible clearance of 0.12 mm (0.005") to the cylinder wall, which is a lot less than 1-2 mm. Normally the cylinder bore would be worn in a tapered fashion (maximum bore size about 10 mm below the top face of the cylinder where the cylinder head mounts), so you need to measure the skirt clearance with the piston at the top of the stroke.
Unless you are wrong about that 1-2 mm, it sounds as if you are in desperate need of a rebore, an oversized piston, and oversized rings to suit. Bearing in mind the price of Honda spare parts, I think the contractor may have effectively extracted the last economically available life from that engine.
Because you are not a contractor, you may decide you are prepared to run the engine with mechanical standards that are not acceptable to Honda, or to a contractor (in other words, reduce the smoke rather than cure it). Before you decide about that, while the cylinder head is off, measure the bore at right angles to the axis of the crankshaft, 10 mm below the top of the cylinder. Compare that dimension with the service limit of 60.165 mm (it measured 60 mm when it was new). If you are very far outside that service limit, this will not be a practical project - but how far is "very far" is difficult to say without experience in that particular engine type.
