Firstly welcome to FT. A suggestion I put forward is you have a lot of reading ahead of you. These topics have been covered a couple of hundred times over here so you can read through other threads but more importantly are the "stickies" in the airline & credit card forums. They give you sweet spots of each program and strategies on smart moves to make.
The upside is you're off to a good start and have plenty of time to earn. The possible downside is changes in programs between now and when you go to book.
A few answers: For many Business cards you do not need to own a company (there of course are exceptions to the rule). Corporate cards do tend to require actual company paperwork as the cards are linked to the corporate and not to individuals for credit ratings. I do believe the INK is one that it doesn't require.
What of the 3000$/month in potential credit card spending is focused on dining, gas, groceries, travel?
Focusing first on the Chase cards it a good strategy since that is where you've already started, it's a high value point system, has many options/bonuses for earnings & many transfer partners.
For where to go after Chase look at the stickies and figure which program will fit your needs. Amex's strength is value & transfer partners. AA has good partners (JL & CX mainly in this situation) but with less options than others.
In Asia LCC can be a bargain or a real PITA with luggage and scheduling. So a flight on TG or VN may be more appropriate for your needs which would make booking partners with those airlines/alliances attractive. This is where Amex MR can pair well with Chase UR.
Another credit card option focus can be for hotels. Hilton has credit cards with Citi & Amex, SPG is with Amex, Marriott & Hyatt are with Chase which may be where you go next with Chase or may be too much with their rules and credit line guidelines. In Vietnam I've found good rates at local hotels that would easily fit the setting of a honeymoon so those you could pay for directly. There is a Hyatt though too but the cost was relatively low. In Bangkok you have the Grand Hyatt and in places such as Phuket you have both SPG & Hyatt properties.
From here I say get reading, do your research, come up with a plan and then come back to us with questions and for an evaluation of your plan.