Well I finished a 2nd attempt and submitted a 1461AD game this time.
Well, congrats.
I learned Democracy in 30BC this time. But this is where my game slowed down some. My cottages were not properly developed and I was short on workers (a bad habit I need to break).
30BC for Democracy is a good date. You should have expected a significant slowdown because after switching to Emancipation you are no longer able to run many specialists (for 6 beakers each), and your cottages are just built, 1-2 commerce only.
So, have some patience. In 15 turns the cottages turn into hamlets for +1 commerce, and in 30 turns more -- into villages for +2 more commerce (one comes from Printing Press). At this point you'll practically restore your pre-emancip. tech rate, and grow further. In 60 more turns villages turn into towns for +3C more under FS.
From this point on you'll be teching faster than a specialist based economy. The only chance for a SE to beat you is to accumulate a significant tech advantage in this period so you'll never catch up. It's quite doable on this type of map, but on larger maps with more grasslands, where you can settle like 10 cottaged cities, you're practically unbeatable.
And yes, you need Workers. Build them cottages in advance, so after Emanc. you have some tiles to work. Forget about mines and production, just work cottages. Your cities must be large enough to work at least all grassland tiles around them.
If you are short on food, build farms while under Slavery/Caste, and set the cities to max growth. After they grow enough, quickly replace all farms with cottages.
Also, use your GSs generated at this time to settle as SS in your Oxford city, to keep your science afloat.
After your cottages are mature, you can also build 1-2 Academies. A super specialist under Rep. generates 9 beakers + 250% (Lib+Uni+Obs+Lab+Acad+Oxford) = 31.5 beakers. An academy in a city with 10 towns (70-80 commerce) generates 35-40 beakers.
Don't forget about Statue of Liberty that comes with Democracy. 1 free specialist from SoL + 1 from Mercantilism...