Personally I'd rig a "Y" bridle of 2 lines down from each cleat, through the bow eye each way, and then to the mooring eye, forgetting the pickup buoy. The dual lines spreads the loading and gives 1 as backup if the other fails.
TIP: Wrap the lines where they chafe the hull with old cotton rags, secured with zipties, same at the cleats. Lines part when the internal temperature (from the repeated stretch and contraction) exceeds the line tensile strength. Oh, and use 3-strand or 8-plait nylon lines, NEVER braided lines - no stretch. The wet rags will help keep the lines 'cool'. Read this in a Boat/US hurricane prep article, with the author (mooring service) stating he hasn't lost a line since doing this.
I also will put a 5-gallon bucket off each stern cleat via a good 10' line, helping to minimize any chafing and prevents excessive swinging, which can unhook traditional moorings (mushroom type).
