The only reason to save them until the end is to make sure you don't bomb some city more than necessary. You can do bombing earlier, as long as you are absolutely certain that it is needed for that particular city. In this case, it's quite obvious that your 2nd and 3rd city will need quite a few bombs, so you could just as well do the bombs immediately. It neither speeds up nor slows down your victory date.
Villages and towns in your cultural cities are not worth bulldozing. You get so much culture from the commerce. Helper cities should have as many farms as possible to max artists.
Running 2-3 artists somewhere probably isn't worth it, except in your cultural cities. If a city is that food poor, better to work hammers and build wealth to press culture slider higher.
You're still building missionaries, are you still planning to build more cathedrals? How many cathedrals have you got in your 3 cities now?
The best thing you can do to speed it up is to get culture slider raised even higher. You can do this by building more wealth, selling resources for gpt to AI, selling old techs to AI for gold and so on. Not sure what you need those grocers for, building them for the gold bonus is not worth it and looks like you don't have unhealthiness problems. Courthouse is most likely also suboptimal compared to building wealth.
Getting rid of unnecessary builds is key to reaching fast dates. Combined with a good game plan and strong micro of course. Here's a picture that shows you just how little is really needed. It's from the victory turn in a 1270AD cultural game I played on noble, showing everything I built during the game.
Scrolling down the buildings list reveals one lighthouse and all the Great Artist wonders + Oracle and AP. AP is also the reason why there are so many Hindu monasteries. (2 cities were culture flipped in the last few turns, otherwise all my cities had temples and monasteries for AP hammers.)
As you can see, no markets, grocers, courthouses or walls. Not even any barracks, and still Peter went down with 4 Horse Archers and a chariot.
(Vicky was killed by my starting warrior on turn 4 or something like that.)
Don't mind the forts and workshops, those were built by automated workers at the end of the game after I had already improved every tile I was ever going to work. And the cottages that are still cottages were captured by expanding borders or culture flipping cities. All cottages I built myself are towns by that date.
To be fair, the screenshot is from a HoF game with quite favorable circumstances, good starting location, peaceful neighbors and a nearby capital to capture immediately, so it's not directly comparable to any random game. But still, it should give you some idea of how little you really need to build to get a fast victory date.
/turn for 4 turns without shrinking. In a golden age those 4 extra artists for 4 turns add up to over 200GPP with NE.
invested in a build, you will get 30 
On the positive side for me: I have A LOT of room for improvement in future games. 
