Henry, Cangrasts on taking the first step. That is for sure the hardest. I applaud you for your thinking in choices you have made so far. When I talk to the investors that I work with, considering new construction is one of the first topics. When doing this you are then owning the home for the best and easiest years of its life. The rate that you are at right now is, I would expect, the main factor limiting cashflow. When consulting investors I have tried to solve for this as well in negotiating with builders to offer rates in the high 3%s. at this rate most properties cashflow nicely.
To your question about the LLC, starting out again you are doing the right thing. The only way to purchase in a LLC is to go with a DSCR loan. This works but the rates for a new LLC are very high. With your first rental, as you learn the only benefit is for liability, but when you are getting started, there are better and cheeper ways to mitigate liability risk. As you say good insurance and adding an umbrella will solve the issue.
Best of luck with this property, If it goes well you will be ready to refinance into a better rate and your next deal when ever we see better rates come back. let me know if I can help.