The 70/120 values you refer to are the *initial* happiness settings. After the capture or hatch event, happiness is only dependant to what is done to the pokémon. Returning them to the box has NO effect on their happiness rating, unless it has been changed (which I strongly doubt - we'd have heard about it by now!). The thing about happiness increase being higher in the pokemon's native area is something I've heard, but never tested. You definitely get double happiness with the Soothe Bell. Vitamins are probably the easiest way to quickly boost happiness; Emerald is the cheapest source for them, from the Battle Frontier - 1 battle point per vitamin - but obviously importing them into 4th edition will be a slow process.
Note that capture with a Luxury ball sets the inital happiness at a higher level (120?).