This is a good point, though I do think that limiting deductions at some generous level will be progressive even within the top 1%. For example, people earning $10 million every year generally have much higher levels of charitable contributions than those earning $1 million a year.
But if limiting deductions isn't progressive enough, then limit the amount of LTCB, interest, and carried interest that can be claimed as such each year to some arbitrary level, maybe $100,000.
The point is, if Republicans cannot agree to a "rate increase" because of their tea party base, change the tax rules in such a way that rates stay the same but the effect of the changes raises the taxes on the wealthy in the desired way.
If it walks like a duck . . . .