Well put, Cordite...
As the History of Technology field points out, it's a mix of factors rather than just one or two. Coal and gears do you no good towards this if you lack the thermodynamic understanding and public acceptance to make efficient use of steam as more than a toy (OTL that knowledge came out of Scotch Whiskey production, of all things). Surplus food and an urbanized population does you little good towards this if it's far easier and cheaper for the Emperor to just put the excess to work making cloth by hand (see China, India, Rome). A wealthy, educated merchant class does you no good towards this if they're much more likely to get filthy rich hauling silk from the orient (see the Caliphate).
Think of it more as a Perfect Storm scenario: you have an excess population driven out of the fields by a revolution in farming methods, a huge and growing worldwide demand for time-consuming-by-hand consumer goods like textiles, an economic revolution that allows accurate accounting of total-value-added cost/labor/time/materials, a large wealthy and independent middle class, existing trade and transport infastructure (canals, roads), new and revolutionary breakthroughs in the fields of thermodynamics and mechanization and metallurgy, revolutionary changes in mining technology, standardized measures, cheap printing and recording of knowledge, public education, and acceptance that advanced learning is actually useful for practical day-to-day concerns. And others I'm overlooking, I'm sure.
Many many many nations and empires in history had SOME of these going at any given time, but only ONE had them ALL: Britain. In order to facilitate an IR at an earlier time you need drastic social, economic, and technical changes in several areas. You can't just plop a steam engine down in front of Caesar and have Roman factories going in a generation.
So I'm sorry, John, but the answer really is "All of The Above" in the truest, most exclusive sense. You need ALL of these factors to generate a true IR with society-changing implications. Having a few can create changes in some areas, but won't a revolution make.