Lindsay, to explain, you said "you're going to have 2 or 3 high commerce cities, giving them academies gets you to Lib faster". I would consider a decent Lib date in a culture game to be something in the t140-t150 range. In HoF styled play it can be faster, on a tougher map it's later, but shouldn't be much later than t160.
So, when are you planning on building those 2nd and 3rd academies? You get the GSs with the help of GLib, so I'd suspect they won't be born very long before 1AD. Let's say you are really fast to GLib and you get that second scientist t105. If target lib date is t145, this gives your academy 40 turns to actively produce science. A GS bulb at this time should give at least 1600 beakers, so your academy needs to make 40 beakers/turn on average. In other words, the second city needs to average a minimum of 80 base bpt. That's not going to happen. Your cottages are not developed enough by then and cities aren't large enough. Even the academy in your capital will have a hard time paying off in time for lib.
Now, you might say that your lib dates are usually later, hence the academies have more time to pay off. But in that case, one reason your lib date is later is that those GSs were wasted on 2nd and 3rd academies.