Believe me when I say this could be the blind leading the blind, but if you can't find more detailed running rigging of Mayflower, another ship of that period could serve you well. The more I delve into my 'San Francisco II' model and want to improve it, the more I find that accurate and authenticated information is simply not present. I'm currently toying with the guns carried by my ship... so far, I've found very little, except that the guns provided with the kit can't be right.
In your case, it may not end up being absolutely accurate, but ships rigged with the same sail layout would surely have similar rigging, especially from the same period, but a mizzen mast will always have had to be manipulated in the same way... so it would need similar rigging, at the very least. As an engineer, I know that compromise is sometimes needed.
I guess I'm saying to broaden your search beyond 'Mayflower'. I'm also saying that whilst it's admirable to find the 'exact' rigging... it may not be possible. More detailed rigging for other ships is a good start. There comes a time when you have to go with the best you have available. I for one, won't be coming to your house, looking at your 'Mayflower' and saying: "Nice... but that double block on the mainsail? Terrible. You ought to be ashamed!"
I'd welcome more knowledgeable people diving in here and telling me why I'm wrong! I'd especially love someone giving you a lovely rigging diagram. I'm a mechanical design engineer. I adopt horse-sense and practical answers where I have no others available. That doesn't stop me seeking accurate answers in the first place. I wish you well. I admire your desire to get this 'right'.