Compromise is a very misunderstood thing.
If one person wants to break up immediately, and the other wants to wait 4 years till the youngest son is out of his teens, the 'immediately' wins, as a practical matter.
There is no compromise when one side presents a flat 'no.'
The woman I am dating wants no children, period. I want four children, and I am open to adopting one or two more if my future spouse is open to that.
There's no compromise there. The 'No' flatly wins. Thoughtless people think that a compromise would be less than 4 children (maybe 1 or 2). In fact, that's not a compromise at all but a complete surrender on the part of my galpal.
The solution (not a compromise) is for one of us to give in, or marry other people someday. It will likely be the latter (but it doesn't stop us from enjoying one another for now).
You have a very practical perspective. There are times when meeting half way is not an option. The compromise, in your case for instance, is to say that you value the relationship over your dream of having four kids.
The emotional trick/self-discipline is not holding that against her later if things go through a rocky period. To give it up completely without any residual resentment. What it all comes down to is that a good marriage is a series of small, but important "little choices."
I come to it as a Christian and I agree with you to a huge extent. In my own life, I must decide daily that I value my relationship with my husband more than "getting my way" every time, or a million other little things. He does the same for me. That is the compromise.
In any case, good job, you've nailed it.