The 4.7m Core sail is only four battens and designed for light weight freestyle and light wave sailors. Therefore it does not have the drive, stability or power for a heavy weight sailor. You will feel every gust in this sail and be constantly off and on the plane. Also note that JP recommend the smallest sail for your 120 board is 5.2m and there are many good reasons for that.
Even if you do get a smaller board the 4.7 Core sail for your weight will still be totally unsuitable. The design of the sail is as critical as the size.
If you are really serious about sailing well in those conditions on a regular basis then keep the 120 board and buy a Kode 94 matched with a new 5.0 Alpha.
Good luck whatever you decide.