I don't think you are fully calculating expenses into your hypothetical 'worst case' scenario. I'm not familiar with the LV market, but a quick zillow search of homes worth 350k puts the average rental value at roughly 2k/month. Since your seller financed PITI is 2k/month, this means you are only cashflow neutral before expenses, and significantly in the red after you account for capex, vacancy, and repairs. Even if you self manage this property you will still be in the red a whole lot more than a measly 300/month.
Also you mention kids, and a second one on the way. Kids are freaking expensive, especially once you start hitting the daycare ages. Being cashflow neutral now may not be a huge deal now, but if your expenses go up then that can be a recipe for disaster.
Also you talk about tax advantages and the deduction only allowing up to 750k. This is largely irrelevant since you specified that you only wanted to live in it for a year and then rent it out. Once you rent it out any primary residence rules go out the window and the interest becomes fully deductible.
Finally you mentioned that taking deductions has limited your ability to refinance or purchase new properties. Any competent lender should be able to distinguish phantom losses due to accelerated depreciation etc, from actual losses. It's not the fact that you are taking many deductions that is hurting your ability to refinance, instead it is likely because you simply aren't cashflowing which is jacking up your debt to income ratio.
Purchasing cashflow neutral homes quickly jacks up your DTI ratio, lets say you earn 6k/month from your job and your expenses are 2k leaving you with 4k to invest. You are doing pretty decent in life and your DTI is 33%. However if you tack on an extra 2k rental income and a 2k expense (in your mythical world where nothing breaks and tenants never vacate), this changes your DTI to 8k income and 4k expenses or a DTI of 50% which makes you ineligible for many loan products.
In an absolute best case scenario you own the house for the full term and save 6k in interest as opposed to a 4% loan at 17yrs. (if such a loan product even exists). Is saving 6k over a 17 year timespan worth the enormous risk you face should things not work out as planned and you need to sell for whatever reason??? If you had to quickly sell, with closing costs you would instantly be in the hole by over 100k. Why risk 100k to chase after 6k??? Why are you so opposed to simply waiting the 6 months to purchase a property? Why not simply wait and find a property that is actually below market value so that instead of paying an extra 6k, you end up saving 30k etc because you bought at the right price, all while also eliminating all of the unnecessary risk. I think you have your heart set on this property because you want to feel like a mover and a shaker and do a seller financed deal. Finding literally any other home in Las Vegas and buying it for 6k under market value would accomplish the same thing without the added risk. This is simply a whole lot of risk all in an effort to buy a property 6 months faster.
I have bought 0% interest deals for more than it was worth, but it was only 10% over retail price and a 30yr loan. In that case it was a no brainer because I was cash flowing multiple hundreds of dollars per month from day 1 and my equity quickly caught up to the retail price.
On second thought buy the house. In a worst case scenario I'll give you a standing offer of 280k cash for when things go wrong. After all, I've been wanting to find a way to make all my vegas trips into a business expense.