Tax options of "not married" and "married state, not married federal" would probably capture all of that. I'd assume that state and local are always identical.
I was confused by "partnered". I took it to mean specifically domestic partners and would have been confused if I were trying to use the tool if I were unmarried but buying a house with my girlfriend or college buddy.
That stood out to me as a specific tweak. Generally, I'd like to see the ability to change some numbers. For example, you recommended that I can afford a house about 20% more than what I actually feel comfortable with, so I'd be more interested in comparing rent vs. buy with the lower house value I'd like to use. I'd also use a VA loan over a FHA due to better terms (no PMI), but there's no where for me to tweak those values.
Although, if you feel like you need to handle same sex couples properly, I should note that there are many times more couples eligible to use a VA loan than same sex couples.
At this point, I would not use the recommendations of your tool. There isn't enough information about what assumptions you make, like how you calculate property tax and whether you are bundling in insurance into the part you assume to be an income tax deduction.
I'd also like to see expected case home price changes, inflation, and investment returns, along with the combination of likely range of returns that would push rent vs. buy in different directions (i.e. good investment returns with low inflation makes renting better, high inflation makes buying better).