The most efficient way of getting gold is to find a job IRL and then buy the gold. Even minimum wage is faster than trying to get it in game.
If you're not into grinding it out in a real world job, the most efficient way is probably to just acquire 2 billion seed money. Then watch the AH and buyout items worth more than 2 billion less than an hour after they're posted. Sell them on the forums, or better yet d2jsp for more than 2 billion. That's probably the fastest way to make billions.
If you really, really don't want to buy your first 2 billion, you can work your way up there by flipping small items and then flipping progressively bigger items. It's a longer haul, though, and you'll likely hit some setbacks when you find you bought something for fair market value or more. If you plan on flipping in the AH at all, though, it's best to get started as early as possible. Compound growth of money and all that.
If you're really, really determined to upgrade your Monk with minimal or no AH flipping, then you should get someone to power-level you a Barb to 60 and start farming with that. It's probably cheaper to make a barb for the most part, and you can use the cash to buy nice gear for your Monk!
Alternatively, you may want to make up some sob story about how your dog died of chlamydia and your wife left you for someone else and she got chlamydia and gave it to you before she left you and how you just lost your house investing in the great tulip bulb bubble and you're writing this all from the military base that you now work in. People may give you some really great gear for free.
Now if you're determined to make all your cash for your Monk by playing only your Monk and without reselling anything in the AH or more than you bought it, you probably want to throw efficiency out the window. You're passing on all the most efficient ways out there. But instead, you can focus on the most fun ways to play your Monk.
Which is really the better question, when you think about it. This isn't a job. Hell, for most people on this forum, it's not even a game. It's more of a hobby. And if your main goal is improving your character, then better gear doesn't make the game easier, it make it harder.. So go make another post about what the most fun builds are. You'll get better, more useful responses, probably.
But if you wanted a simpler answer, then... yeah... It looks like you're TR farming with your gear. That's an OK way to go. Do that over and over on low MP if you enjoy it. It works pretty well.