Okay, here's a first attempt. This can probably be improved on but it will give others a baseline to work with.
Open Island/Silver
Turn 3 (Copper x5) - Buy Throne room.
Turn 4 (Silver, Copper x2, Estate x2) - Buy Island.
Turn 5 (Island, Estate, <shuffle>, Estate, Throne Room, Copper) - TR Island, set aside Estate x2.
Turn 6 (Copper x4, Silver) - Buy Island.
Turn 7 (Copper x2, Island, Estate, <shuffle>, TR) - TR Island, set aside Estate, Copper.
Turn 8 (Copper x5) - Buy Island.
Turn 9 (Silver, Copper, Island, <shuffle>, Copper x2) - Buy Island.
Turn 10 (Island, TR, Copper x3) - TR Island, set aside Copper x2.
Turn 11 (<shuffle>, Island, TR, Copper x3) - TR Island, set aside Copper x2.
Turn 12 (Silver, Island, Copper, <shuffle>, Copper, TR) - Buy Island.
Turn 13 (<shuffle>, Silver, Copper x2, Island, Island) - Buy Island.
Turn 14 (TR, <shuffle>, Island, Copper x2, Silver) - TR Island, set aside Copper x2.
Turn 14 (Island, Island, <shuffle>, Silver, TR) - Island, set aside Silver.
Turn 15 (<shuffle>, Island, TR) - Island, set aside TR.
Whole deck on the Island mat at the end of turn 15.
(I have probably made a mistake somewhere)