Hmm... Gunpowder and paper IOTL spread very quickly. Hard to see them spreading much more quickly, as did the navigational compass. They're all things that can spread fairly easily by trade routes on ship or caravan, and technologically they're immediately very useful at almost any level of navigation or sedentary society.
Printing happens, probably independently, pretty much as soon as paper spreads and production gets to a level to make mass production economical. It's just an obvious idea once the scale of production is about.
Other Song inventions seem harder to imagine spreading because certainly Europe and probably the Near East and India of the mid 10th to early 12th century did not really have the commerical society required to sustain or need them. Probably ditto Japan of the time. Restaurants in Europe of the High Middle Ages?
Paper money is another example of a Song invention, but it's hard for that to happen unless you have paper and printing first, a shortage of metals and any kind of plausible agents to act as a guarantor.
(Without being a Goldbug, you could question whether paper money necessarily had any long term positive effects over the longer haul, and so whether this would do much good for the world at large. Periods of hyperinflation and problems with multiple competing currency standards may have been consequential on innovation of paper money.)
Song type porcelain is somewhat imaginable to spread more than it did? That mainly requires an understanding of vitrification and kaolin to spread.
I guess it's hard to talk about this topic in general without specific innovations in mind.