"estimated tax payments due from each beneficiary"

What alternate universe are they living in?

Are the payments for the beneficiary's 1040, or for the trust's 1041?

Sometimes a trustee will make part of a required income distribution in the form of an ES payment to cover the tax the beneficiary will owe when they report K-1 income.  But that doesn't seem to be what's happening here.

Sounds like another case of "I don't care what the law says, I'm going to have the trust pay the tax (at higher rates) and just let the beneficiary keep the rest, so there is no K-1."

Is your client the first to reach 35?  So the other two (probably siblings) are being screwed over for another few years?