"Depositor" isn't a valid term. You mean Grantor, which, if deceased, can't do anything.
No I believe it wouldn't be a sham if, as a Trustee, you simply did the transactions through a 1031 exchange. No real way of "removing" it from the (now irrevocable) trust without considering it a sale, so just sell it and buy another ("replace") property within the 1031 time constraints.
