RCP @3 and @6 seems a little crowded for me.
My suggestion is Ring one at 3, 3.5 or 4 pending on terrain (if one city is on a cow @3, we won't build at three. We should build at least 6 of the possible 8 cities in the first ring (we could skip/delay the cities with worst positioning.
Second ring should be somewhere between 7 and 9, again depending on terrain. We should build a lot of cities there: at least 15.
Rough building order should be:
-turn capitol into settler factory (granary).
-build settlers in capitol, workers in Ring One
-build another one or two settler factories in Ring One (best sites), and barracks/ military/ more workers in the remaining cities
-build military in Ring one military camps and workers in Ring two cities
-build military everywhere
When done building rings: upgrade military -> attack -> Golden Age -> More military -> Get half the map -> upgrade again -> attack -> end game at Cavalry the latest.
From this perspective I'd like to play either Iroquois or one of the nations that have the UU at Chivlary. Egypt is also possible but a little risky.
Bear in mind that this would work if applied consistently