You’ve done a lot more assumption guidelines than this simple counter, but this counter measures the rate of vaccinations per day to get how long it would take to get the country to 70% vaccinated. When I originally posted it in the breaking news thread on Jan 8, the time to herd was 1,195 days.
Today, 4 days later, the time to herd is 711 days. So the rate of daily vaccinations is definitely increasing.