I find it strange that you seem to describe this ashelping you get signal in the town as well as home... you would need a wifi connection for that.
The Note3 doesnt support this feature (or EE dont) so your now relying on the mobile signal, which it seems is not so good in your area.
EE do however have a femtocell (Signal booster) that plugs into your home broadband and acts as a mini base station, you may be able to persude those on 150 to provide one of these as your signal is now bad.
However, I suspect that it will be an uphill battle explaining to them your reasoning behind upgrading when the signal in your area has always been bad. You need to make sure the person you speak to knows what UMA/Siganl Boost is to stand a chance