Well, there is really no telling what we could do if we had massive popular support for ending birthright and demands for a reinterpretation of the 14th amendment - but getting that kind of groundswell of support would be very difficult given the divisions within the country.
If we had such a surge of support, I suppose the Executive branch could do as you suggest, the Legislative branch could agree (this assumes we have pretty overwhelming Republican numbers in both chambers) and 2 of the 3 branches of government could just tell SCOTUS to sod off.
You would really need to unite Republicans (to include almost all whites), union workers, a good chunk of blacks, etc, to do it though. Rare moments in history happen now and again, but this scenario of mine is more pie in the sky than anything else.
It would be nice to tell the Supreme Court to take a hike though. They could issue their rulings and the other 2 branches could laugh and ask them how they intend to enforce them. Though fun to imagine, I think we both know the odds of it happening are about slim to none.
Changing out the justices is the best I can come up with for the birthright issue. I suppose if we had the numbers we could impeach the liberals and replace them. Or, a conservative President could threaten to pack the court like FDR did to make them go along. I suppose if that doesn’t work, he or she really could add more justices. There is nothing I am aware of that enshrines 9 justices as the end all be all on the SCOTUS.
As a side, what gives the scotus their power is the rule of law. The fact that this nation is bound by, and behavior based on, the Rule Of Law, and not legions of military force.
It has come to pass that they use that ROL as the very source of their perceived power, making "lawful" declarations that must stand.
It is the same tactic libs have been using for 60 plus years, hiding behind the ROL, shopping for crooked judges that uphold the whim of the few, not the will of the people, knowing that "lawful" conservatives will obey.
It is time to force the issues. It is time for our side to in effect, laugh at the supremes, and ask them what are they going to do about it.