Well said, but that the federal government would try to stop or subvert it is kind of obvious. In truth, I expect that if the SCOTUS involves itself at any level, that is, does not firmly refuse to hear any appeals about the convention, and even goes so far as to instruct the judiciary that it is not their business, there is going to be trouble.
The federal judiciary has no authority over a convention, and if the convention votes it, any federal judge who involves himself, as well as any federal agency or individual, can be immediately suspended or even arrested.
That point should not be neglected: that the convention may sit as a judge and jury, and basically order villains to prison for an indeterminate length of time, while they accomplish their purpose.
I've not been able to find where a Convention of States called for the purpose of proposing amendments has that sort of authority, but I think a more likely reaction by the Establishment (including the judiciary) would be to quickly pass a few placebo bills, hoping to take the wind out of the delegates' sails, and I wouldn't rule out an attempt to propose a new "omnibus" amendment themselves... anything to muddy the waters.