It is doable, but here is my caution.
I have had listings where the seller has asked contractors / friends what they think, will their home sell? The answer always is "Yes, I would buy it. That seems like a no-brainer." The problem is that person usually is NOT a real buyer. It all sells eventually if parties are willing, just often not at the initial price. I don't know about your market - but there are so few buyers in my market, great homes are just sitting, even at lower price points, and we are still faring fairly well compared to the national average.
Considering BAC, you should go find an agent that will actually do both ends of the deal - they are few and far between - those willing to be the only agent with a FSBO. Even with myself included, in my metro area (the whole Portland - Vancouver area) I have only see two handful of other agents / brokerages willing perform that. When dual agency gets created your Realtor turns into a facilitator and a messenger since negotiation as a service is lost per state rules (your state might be different). It cracks me up EVERY time whenever a person tells me they are planning to only use one agent. I save my clients MORE than my fee. I always think, "Dodged a bullet there, cause they just told me they are smarter than me, lol.
FSBO with BAC is doable, but it is not for the feint of heart. I am straight up with my Buyers, when I tell them that the state requires me NOT to provide negotiation as a service in a FSBO scenario, many tell me they want my expertise, and that is what they are paying for. I have also found that many FSBO sellers have unrealistic expectations and don't have the experience of the industry to know what is the norm. And that works against them just to save a few bucks initially.
I have listed good homes that sit as FSBO 3-4x market average that sell quickly once listed and there are two agents in the deal. I would recommend looking at an agent like a paid friend where you should be willing to accept the truth from (that is why not every agent is for every person) who has access to marketing tools and negotiation experience. Maybe hire an attorney to help you instead, at least you can get negotiation experience.
Lol, last year I had buyers who put an offer onto a FSBO, where the seller verbally said he would fix items from the inspection though he was unwilling to put that on paper. Well you know where this deal went? Into the toilet. He was calling me every month for three months after asking why it failed. I gave him the same response every time, "You were unwilling to put it into writing the items you verbally said you would repair. So they buyers went and bought elsewhere." The back-end is that he kept agreeing to fix things, verbally, because he wanted to be done with the property, but then would go talk with his wife and she would beat him up. These weren't outlandish requests.
I had another I listed, where three offers came without an agent, back-to-back, so dual agency got created in these scenarios as well. In all three, when the deals failed after defects were found that the seller was unwilling to pay for, the seller kept asking me why he didn't get to keep the earnest money even though I explained it AND it was in the contract. Imagine having the same exact conversation three times, lol. Here is another chuckle, when I listed this property, I said, "Ok, this price is a good starting point. Just be aware, if we get an offer and defects are found, the price usually goes down." So we get an offer, and the seller counter offers at a higher price than the list price. His reasoning was that he would raise the price after getting an offer to deflect defect costs, as this was a "starting point". The buyers actually agreed, but then it did eventually fail because of defects. Property finally sold but at 65% of the list price from all the defects found along the way from other contracts.
The most recent buyer I represented with a represented flipper, they got the home for 82% of list price. Negotiations!!!! I always maintain the walk-away factor.
Looking at the scenario, is your down payment correct? You can only have one primary residence. Is your wife comfortable with it being a construction zone? 5% down is a personal residence. The lowest I have seen with an investor loan is 10%. Also if it if personal, remember you only get the personal exemption once every 2 years +/-. Since you are buying another house, are your numbers right?
Here is my reco - buy the home with the worst case that you get stuck with it for a year. And if you can get out from underneath it sooner - BONUS! Be sure to include utility costs and insurance costs too. New appliances seems low too. PMI prepayment cost? Closing cost is appropriate imo. I am usually cautious whenever I see 00s in projections. GO find the actual numbers.
And then compare that against how you can use the money in other ways. Essentially, you are buying something for $46,000 to sell it at $69,000. Then take capital gains out b/c it is short term gain, so you lose $4,600, with a gain of $18,400. $46,000 + $4,600 = $50,600 true cost in your scenario, or $18,400 in profit. If it goes south, you are underwater in 12 months just from the mortgage payment, since the first mortgage payment usually comes 45 days after the loan is closed.
That is a good enough return according to my standards but with it comes a LOT of work, and my wife would probably kill me just from the stress of it and all the other projects going on. Then I gauge this against other income streams, and in that case it is just not worth the stress for the money. The biggest problem really is that I don't trust those numbers.
Good luck!