If it were me, agency commissioners elected by popular vote to a six year term, subject to recall by vote and impeachment by Congress. But that's orthogonal to the purpose of the branch.

If you're suggesting a rogue government with the ability to deprive such independent organizations of funding as a means of control, you're not wrong. If the government and people united have enough of a majority (or enough lack of accountability), laws are as valuable as the paper it's printed on. Leaving the latter aside, it's also just models from the federal constitution that (nearly?) all state constitutions tend to be living documents. Nothing is truly set in stone and most mechanisms tend to have overridde mechanics with a majority or supermajority.