We will finish horseback riding this turn. Our allies have:
Kaz: Aesthetics, Archery, Metal Casting
Cav: Currency

San and Sat both have Archery, Metal Casting, Currency, Feudalism

We are up
Hunting on Cav
Poly and Math on San
Poly, Civil Service, Calendar, and Construction on Sat

Therefore our alliance is up at least HBR, Construction, and Aesthetics, and down Feudalism.
I don't think there is anything important after Feudalism that San and Sat might have. Can anyone confirm that?

Our research opportunities
Feudalism 1046, 11 turns
Theology 747, 9 turns
Aesthetics - trade
Currency - trade
Philosophy 1196, 13 turns
Paper 897, 10 turns
Archery - trade
Metal Casting - trade
Compass - useless unless we want a suprise attack by sea

After trades
Machinery 1046, 14 turns

This is timely -- Kaz have suggested the alliance research Machinery, Feudalism, Paper. They would like to take Machinery.

I'm going to do the following:

Ask Saturn if they have any interest in Civil Service for Feudalism+Archery.
Ask Cav and Kaz if they object to the trade with Saturn

If no trade, which do you prefer - Feudalism or Paper?
If paper, maybe we should aim for Liberalism first?

Good post.
My opinion
Compass isn't useless, because with currency we get 2 TW each City and a harbor gives us +50% (most +0,5) sometimes (often) +1 (round down).

Btw
We 've cs, are we in bureaucracy?