Most important thing is that USA doesn't do Pax Americana. That means you should go historical because with historical off this focus is chosen quite early.
Second thing is the order of conquest.
I did it in this order:
1. Venezuela
2. Ecuador
3. Peru
4. Panama
Panama was a close call. I brought them to capitulation only a few days before any major power (mainly UK or US) could intervene.
My divisions were mainly width 20, 1 ART rest INF and support set to ART and ENG. Add some MAINT (equipment capture) if possible.
Venezuela requires a lot of micro management. First let them bleed dry on your defenses (I didn't build any forts, wiki says you should - your call. I prefered building MIC) then encircle them. Not that easy because not much room for maneuvers but possible.
Ecuador should be a walk in the park.
Peru is a grind because of the mountains but besides of that not that different from Venezuela. Well besides the fact that both (you and your enemy) will have far more troops than you did with Venezuela.
After that I focused on Panama because I almost expected the USA to intervene (as said, they didn't) and Panama had its troops (one or two divisons) on the far side of the Canal so I could have done that some time in between with a single division...
I cannot recall exactly how I did my DOW management but I guess I didn't have much peace between those conquests. I think I started to justify when I thought I had pushed far enough and decimated the enemy sufficently so I could remove some divisions to another front to start building up planning bonus.
After conquering Peru I began to exchange my coastal MIC to NIC and started building BB - just build the earliest models, they're the cheapest and thus fastest completed.
When I had 30 NIC I used 15 to build BB and 15 to build CV, set the game to speed 5 and took a nap (not literally but you get the point

).