It seems to me the 4 year campaign was key to do the transition successfully.

> In 1963, the Riksdag approved the change and established the Statens Högertrafikkommission (HTK) ("state right-hand traffic commission") to oversee it. It also began implementing a four-year education program, with the advice of psychologists.[1]

> The campaign included displaying the Dagen H logo on various commemorative items, including milk cartons, men's shorts[1] and women's underwear.[2] Swedish television held a contest for songs about the change; the winning entry was Håll dig till höger, Svensson ('Keep to the right, Svensson') by Rock-Boris.