In a Democracy, I always use 30% Lux in late game, and Tax/Sci battle it out for the other 70%. This will keep almost any city growing, provided it has the basic happiness improvements commensurate with the difficulty level and city size. The object is for the city to reach it's production (shield) potential as quickly as possible (all my comments refer to whatever style and game situation is going on, e.g., none are ever blindly geared to achieve a score, as is the case in GOTMs... but many of the basic strategies are not altered at all for an all-out, down in the dirt Democratic war
).
So I see no reason in this game to leave Democracy, nor drop below 30% Lux (and keep the size 11, 12, 13, 14, 15, etc. cities going up to size 19 or 20, minimum). Citizens above #20 (assuming a city is using all 21 tiles) can often be better used as an Engineer instead of a taxman or scientist (except for the SSC, which usually needs all scientists and no engineers supported).
The remaining 70% should be determined by how much science remains before the next advance. Example, if 245 beakers remain, about 10% would probably do (use F5 and scroll to bottom to determine beakers necessary for the next advance, and compare it to the beaker output for a given slider setting).
If a sudden need for gold arises, just max it to 70% tax (e.g., a city bribe or essential rush builds)... the science can wait a turn or two.
Since the exact split of Sci/Tax is a turn by turn dynamic thing, my vote on that setting is whatever teh President decides as the turns are played. Plenty of turns remain (we're only in the 1800's), so my bias would be to keep taxes higher (based on what needs to be rushed and bribed), and deliver Freight to fund science at a somewhat leisurely pace.
Any Freights that are delivered should have SHs in the source city, and Airports in both cities... if not, wait a turn until those cities can get the improvements rushed... this combination will
double the value of a delivery, which in turn doubles both the gold and beakers! This is typically where I usually spend
vast sums of gold (rush buys) in a rapidly growing warlike Democracy.