You said the time value of your puts is zero or near zero. That's probably why you get assigned. I think if time value is near zero, then the long option holder can exercise the option at no loss of time value. If your goal is to get exposure to the S&P 500 with little capital requirement, why don't you just buy /ES or /MES futures? Another possibility would be to sell at the money options, which typically have about -0.5 delta.
I'm going to tell you a secret. The futut ES contract loses one point per month automatically. You cannot be long in either a synthetic position in options or with the future without losing 12 points per year. The only way to go long without losing money is to buy the spy directly but this monopolizes too much money to make arbitrage interesting against a synthetic short position as an option. It earns a guaranteed 4% per year but that doesn't interest me. I cannot sell PUT otm options because on the SPX the option is worth less than its intrasec value and with the spy, I am exercised. If there is a solution, it would bring in a guaranteed 10 to 15% per year.
when you account for the opportunity cost of funds. That a future only requires a tiny amount of margin and the rest of your cash can be put into the risk free rate, it’s all the same. there is no guaranteed 10-15percent/year.