mooring rope recommendation

Personally I think you have too many lines on. If, as I suspect reading between the lines you are using a mooring buoy you want one strop (bridle) over the bow and a safety line in case it breaks slightly longer. You need to rely on the catenary of the mooring chain to provide shock absorption to any rough weather so your strop should be short enough to partially lift the mooring buoy. i.e. always under some tension. A good rule of thumb for length is 1.5x the height of the bow from the waterline. Adding lines promotes fouling and can induce momentum snatch and shock. Securing the lines to the tow eye is the worst possible idea, especially with a carabinier. Obviously you need to ensure your cleats are up to the task. Many are not and are designed for pontoon mooring. Strengthening those should be a priority.

If you dont have a central mooring cleat and bow roller you will need a bridle ( Y ) . The ends of the strop should be spliced into an eye that just fits over the cleat (i.e. eye = ~ 2/3 the cleat length) the end that connects to the mooring chain should be spliced round a rope thimble and attached via a D shackle which is secured from unscrewing with a mouse wire (stainless steel seizing wire) preferred or single use nylon zip tie will suffice.

Whoever said anything about not using nylon got it wrong. Nylon is what you want in a mooring strop and it does have some stretch. You want to sleeve the strop over rubbing points to prevent chafe. This can be either plastic tubing or canvas socks. Make sure they are secure and cannot slide up the rope. Finally you are best not using nylon 3 strand as this rope can cockle as it spins round the buoy. (unravel or tighten) You are best using nylon octoplait / anchorplait etc that is made from 8 or more strands. This will not cockle.