That is a tough scenario. I think that what you are trying to do is spot on, minimizing (or negating) your housing expense in order to bolster your saving and investing power. Unfortunately, as already pointed out by @Nathan Gesner, you are putting yourself in very precarious position if anything goes wrong and you have deployed ALL of your capital (plus some in this case). And not just with the house, what if your car breaks down? What if you need to take some emergency leave for yourself for a family member? Ect, ect.
The most prudent thing to do would be: Find a nice but inexpensive rental and then live below your means for about a year, maybe you have a buddy who is trying to house hack and you can rent a room from someone else. Save all you can. Go to Mr Money Mustache website for some aggressive (arguably too aggressive for some) methods on cutting the spending so you can put some money away. Save up an emergency fund (3-6 months of liquid cash, how much will vary based on who you ask/read), then put everything that is left into an account to save for a downpayment, closing costs (although asking the seller for closing cost assist is also a great plan), and some reserves for whatever "little" issues come up with the house.
Then come back to it in a year and you will be in a much "safer" position.
Best of luck.