This does not answer your direct question on how to change the proportions. Instead it just solves the problem. Simply buy a bottle of molasses, and then you will never need to consider this, because you can create the brown sugar from white sugar with molasses.
They are 100% interchangeable with a little trick. First, let's have a look at how brown sugar is manufactured. It's just white sugar mixed with molasses. Yes, that's actually true. There's nothing magic about brown sugar. You can buy the molasses separately. There's no need to buy it premixed.
A drawback with brown sugar is that it becomes like a brick after a while. It's much harder to store for a long time than white sugar. So just buy some molasses, and whenever a recipe calls for brown sugar, use white sugar and molasses. Molasses also lasts virtually forever, so just buy a bottle. This also gives you the benefit of being able to mix in more molasses without adding more sugar if that's what you want. It's like if a recipe calls for salted butter, then you can use unsalted butter and add some salt.
It works very well in all situations I have come across. Not only when you want to mix the brown sugar in a dough or something else. You can also very easily create brown sugar on demand to use for topping. Just put white sugar and molasses in a mixer and * poff * you have brown sugar.
To be honest, since I discovered this, I see actually no reason whatsoever to buy brown sugar. So buy a bottle and never have this worry again.
Here is a good video explaining it: https://www.youtube.com/watch?v=LF8cWXlNSEM