I'm already aware of everything you mentioned. The blood moon "offset" setting that I am proposing is separate from what is available.
Quitting and changing the settings is my current solution as I said, but it is a clunky and immersion-killing option.
If it's not clear what I'm describing as the offset, here are some examples.
Default
Blood Moon Frequency = every 7 days
Blood Moon Offset = 0 days
{7, 14, 21, 28, 35, ...}
Default but delayed by 1 day
Blood Moon Frequency = every 7 days
Blood Moon Offset = 1 day
{8, 15, 22, 29, 36, ...}
First blood moon on the 7th day, then every day onwards
Blood Moon Frequency = every 1 day
Blood Moon Offset = 6 days
{7, 8, 9, 10, 11, ...}
First blood moon on the 7th day, then every 3 days onwards
Blood Moon Frequency = every 3 days
Blood Moon Offset = 4 days
{7, 10, 13, 16, 19, ...}