From what I gather, the zero meridian was not really fixed on Greenwich until the early 1900's, or rather, every country with some naval power had its own reverence point with its own maps showing longitudes in reference to this point. Famously when Jules Verne wrote "20.000 leagues under the sea" in 1870, Captain Nemo always lets professor Arronax choose whether he wants to know the position according to the longitude of Greenwich, Paris or Washington. (Mostly, he continues with "In your honor, I will use the Paris meridian, according to which we are now at ....") For the captain, as for pretty much any trained sailor switching meridians was an easy thing to do. You just added or subtracted a fixed number. It's not that much more complicated then switching from US eastern time to US standard time to Greenwich Mean Time. Certainly a lot easier then switching from miles to kilometers or from Celsius to Fahrenheit.
In short, longitude was never given as an absolute number, rather as a relative number to a reference point. It was only when the British Admiralty maps became the prevalent standard that everybody ended up using the maps and therefore the corresponding median.
So how to get to a different meridian? Stop the UK from becoming such a naval power, or simply from becoming so great explorers and mapmakers.... At least until navigation becomes so fine-tuned as it became between 1800 and today. With a combination of better navigation aids, sextants, clocks and maps, and a less naval UK, we might well be using the meridian of Madrid, Lisbon or even Newfoundland right now.