How does one conquer Native Americans and not loose diplomatic points?

So I am playing as Florence and thought it would be interesting to establish a foothold in Mexico. So I declared war on one of the smaller nations to gain some land first before I continue. However, it seems that they're all connected through vassalisation so actually the result was that most of Mexico declared back. I was easily strong enough to beat all of them and win the war.

But the fun started after the war. In the peace treaty I took Tenochtitlan as well as many other provinces (as many as I could since I assumed that they would become a colonial nation as soon as I have at least five of them). That not only resulted in massive overextension of 114%, but also granted me the "privilege" of taking Aztec vassals as my own vassals. Now I have 5 new vassals in Mexico, which along with all the other relationships in Europe adds up to 9 diplomatic relationships in total.

Overextension I think I can manage by coring five provinces, and letting the colonial nation deal with them. However, having so many vassals has killed all diplomatic points that I generate (you loose one diplomatic point for every relationship over the limit, in my case limit is four so I am five over the limit). To make matters worse I am not allowed to release them until the peace treaty expires. In 15 years...

So is there any way for me to avoid not generating any diplomatic points for the next 15 years? I should add that I am playing ironman. Was there any way for me to have avoided this fate altogether and still conquered Mexico?