Would you fly Copa or Avianca to get to your US departure city? That might get you more options, and potentially avoid very long layovers or airport changes (e.g. with UA, changing from EWR to JFK).

You don't have to have the same operating carrier for each segment, so if you want to use NH for your TPAC segment to TYO, look at *A carriers to get you from BOG to wherever the NH flight departs from. Copa, UA, NH, and Avianca are all in *A, so you probably could get a ticket to price BOG-TYO via the US as one ticket.

Using your dates, I quickly pulled a BOG-PTY-LAX-HND-LAX-PTY-BOG itin that priced out on ITA for under US$1300 (But an overnight layover in LAX on the way back). BOG-PTY-LAX and return were on Copa, and the LAX-HND-LAX legs were a UA codeshare operated by NH. Using other gateways and NH were in the neighborhood of $1500 for BOG-us-TYO-us-BOG.