Coming from a fiscal conservative, here are my thoughts...
Take care of your family first. Pay off your debts first. Those hang over you like a noose. The first thing that I would do would be to pay off the student loan. You don't disclose loan rates, but if you are close to finishing that up, I would do it. Accelerate payments, less owed. I don't know your tax situation in Australia, but sometime here in 'murica it might be tax advantaged to keep a mortgage payment for tax purposes.
Kids are expensive.
Stop the multiple lines of thinking. You have already given up on NT buffalo. The North America tag game is to me unreliable. DIY? Might be cheap, but you will probably have no advance scouting as you would have limited time and no awareness of the area. I wouldn't do it unless you had access to a person/land owner who could help you out with scouting and guidance. I wouldn't put any money in that fund unless there was a solid partnership. Also include airfare to Africa vs. USA in the final tally. In my simple thoughts, an African trip is the best money to put money on.
Is a second job possible? How much will that impact your family life? Wife willing for you to be away to fund your hunting trip? Budget differently? What are you and the wife and kid and possible future kids be willing to do without you so you can be out hunting and everyone's still happy and safe?
You state that you don't dote on birthdays but then you state that you want to do a special hunt for your 30th birthday. Request a donation for hunting funds for a future African hunt. Put the donations in an interest bearing account dedicated to your trip if that meets your family's financial needs at the time.
You are relatively young. Get your financial house in order first. Provide for your family and future family. Hunting and personal other personal preferences come second.
You are pretty young, and you are thinking right from what I can read.
Steve