IHT: Well a few things. Many of our cities were unhealthy, so I threw in some harbors and aquaducts. Our spies were all in Peter's land, NOt Capacs.
I swap a few things, actually, more than half the builds. We want Marines, not Tanks. Get some more Navy started.
Disband some ancient military.
Turn 1: I spend 200 gold and blow up a spice plantation in HC's land. WOOT. Stuff builds, etc.
Turn 2: More stuff builds, Heavy Infra pushing.
Turn 3: We get Fusion, A GE and a Golden AGE!! Research to get us a fridge so we can store our beer.
Turn 4: Actually get a Missionary to spread religion. YaY!!
Turn 5: Workers are doing a Civ3 Style RR JOb now. Moving ships around to prepare for trouble with HC.
Turn 6: We have a GE by Istanbul
Turn Whatever: A good portion of our Navy is by Zaragoza.
Turn 9: I know this is generally bad SG ettiquette, but HC converted religions to Taoism, and I could buy in Peter and Toku. So I did!!
I have been building a bunch of jails, I have Rushmore going, and I have been sneaking in temples and such.
I also pillaged with spies a lot of HC's resources, dropping his trading relations.
Be advised we are not yet at war, but could be really soon like!!
Turn 10: we build the internet. (Inserts the video "The Internet is for Porn"

)
Anyway, thoughts: Keep using spies to really Mess up HC. Keep some Marines coming, along with building airports for trade and troop transit to the other continent.
Toku build his apollo, but we shouldn't have to worry too much.
Health, and then happiness once the war starts will be key.
When the war starts, use our ships and Marines to take a lightly defended city on the coast, then ship over some modern armors and Mechs. Then it is pretty much game over man for the Incans.
Other random thoughts involve utilizing our many Janissaries to Defend by Volume, if we take a city from the Inca. Otherwise we may wish to disband them.
We got flight, satellites and composites on my last turn from the internet, so there are probably some SS parts to build now. We get genetics next turn, so that will help quite nicely as well.
http://www.civfanatics.net/uploads11/T_McC_AD-1920.Civ4SavedGame