If retaining the ability to have more kids is so important to you, even though your wife has stated that she is 100% opposed to having more kids, then I think you need to assess how committed you are to this marriage. Not meant in an accusatory way. Merely stating the facts as they appear to me from your post.

You could have more sex next week if you got a vasectomy tomorrow. But you refuse. To me, that says you value the possibility of more kids higher than you value sex. Without sex, you realize that your marriage is at risk of failing. So by refusing to get a V, you are implicitly valuing the possibility of future kids higher than you value your marriage.

By refusing to get a V, you are implicitly saying to your wife "I am not sure I am going to remain married to you, so I want to keep my options open. I might meet a woman who wants more kids. I don't want her to reject me because I got a V." I can easily understand why your wife is rarely in the mood to have sex with you if she imagines you are thinking what I just wrote.

Look, the years when you have small kids are often tough on a couple's sex life. You brought another baby into your life just when the older kids are becoming less needy and you might have had time for more UA / each other. Your choice. Now you need to deal with the consequences. When you add the "I will not get a V", it makes it that much harder.