So I have a series of weird flights I can use to get to Bangkok from London with a stop in Vancouver, where it may actually be cheaper for me to fly to Vancouver, bus down to LA/San Fran, and then fly to Bangkok, or fly to LA, bus to Vancouver and then fly to Bangkok.   

Regardless, I've been told there may be problems with a one-way ticket into the US or Canada.  Would it be enough to simply buy a greyhound ticket to show you're leaving the country to your new destination?

Eg:

Fly LON->Vancouver, with greyhound tickets to get me to Los Angeles (or a short flight, yet to decide).

Fly LA to Bangkok.

Presumably in this case I'd simply need to show my onward ticket for each country, be it plane or bus?

(New Zealand passport)