I Don't understand why you are mixing your finances and your father's. If you intend to take this $350k in return for your $1,000, do you have an idea of the formal contract you would sign? Or would you intend this to be informal? (I would not recommend that, by the way)
Your father seems to have things in hand. 4% of $350k would be $14k per year, so withdrawing $1k per month sounds perfectly prudent. If he is willing to do this, why complicate things? More likely than not, there will be plenty of money left when your father passes. And in the meantime, you will have your full payout to invest, if you wish.
If your father is not so risk averse to try a prudent withdrawal rate rather than being stuck on annuities, then let him do it. I would be very concerned about mixing that much money with family relations. (both your father and sister) Fallout from misunderstandings / changed minds / differences of opinion also has to be considered with family finance.
Having said all this, I think it is relatively common to have a parent write a mortgage for a child. This type of arrangement addresses a lot of the shortcomings I mention: it is fairly straightforward to have a formal contract, with standard conditions that are easily understood. If someone fails to hold up to the commitment, there are clear remedies. (although, of course, there is still the risk of family drama / manipulation) Could either you or your sister refinance to a mortgage note held by your father?