Last year, It cost me around $450 to convert a ? 2005 model to a 6 speed one. The hub gear is not compatible so Bike shop suggested I replace it with a new rear wheel/ gear.

I suggest you resale the bike and buy a new 6 speed. I find the old 3 speed brompton doesn't have the nice ride as the new 6-speed - too slow for my liking and not good with hills in my area.