Ok, so i did those 3 more turns:
turn7:
-Trade Medicine from America for Industrialisation.
-Sell Medicine to France for 280 gold + 31 gpt (where are they gonna get 31 gpt with only 1 city
)
-Sell Industry to germans for 1090 gold
-Buy Electricity from Russia for Industrialisation + 960 gold
-Get Nationalism from england for Electricity + Industrialisation
Research on replacable part at 80%, due in 9 turns. IMO this should be the last thing we research.
Turn8:
-Upgrade most or all Musketmen to riffles this and next 2 turns.
-Disband non elete obsolete Legionaires.
-Sign peace again to stop war weariness and allow a 0% lux slider.
Turn9:
Aztecs and Amerca sign alliance against us. No real danger here, only 1 aztec galley in the south.
Turn10:
Sign peace with aztec, they throw in 25 gpt, i throw in Industrialisation.
As the realroad network is starting to grow into existence, i am moving almost all units northwards except for a few in the south eastern area where RR is still some decades away. When realroads are ready, cities don't need to be defended anymore, a small interception force can then use the RR to cover the whole empire.
Forces are now gathering to move to New York, but if it seems to hard, it is not so important to take it now already. We will soon have the ability to upgrade all our cannons to artillery. With those, we should be able to conquer any city on our continent, regardless its defence or underlaying terrain. Maybe you want to wait for that before attacking america (or any else) and make the troops move to one of our (northern) cities for upgrade by the time the research is done. Barracks can be rushbuilt for the upgrade the turn before the research is done.
I suggest relying on the artillery from here on. If there is anyone who never used it yet:
the idea is to have some strong defenders, possibly an army with defensive units in a stack together with a large amount of artillery and a few offensive units. when moving trough enemy territory, the cavalry can move out of the stack to attack or take workers in adjacent squares, then move back into the stack where they are safe. When reaching a city, the artillery should first redline every single unit inside it before the cavalry attacks what remains of the units.
It is important to keep the stack together and to have a decent sized stack. The units cannot be spread over the map to much. I think we can make a few of these stacks. A stack should contain for example 15-20 artillery + 5 defenders + 5 attackers.
Obviously we have more than enough attackers to make some stacks, but only artillery and defenders for 2 or 3 now. Therefore i suggested making more of those. Lost or wounded units in the stack must be replaced or waited until they are healed.