"do the dividends earned by the Roth IRA which are then reinvested count toward the $600 gross income threshold?"
No.
If the terms of the trust permit, the inherited Roth IRA maintained for the benefit of the trust could be assigned out of the trust to inherited Roth IRAs maintained for the benefit of the trust beneficiaries and the trust could be terminated. Of course if the intent is to not make any distributions until year 10 (when certainly any distribution would be a tax-free qualified distribution), it's probably no extra effort to maintain the trust until then.
