Is there any way to tell a miner "Do not include my tx before 2am UTC"?
There isn't as of right now. An EIP about account abstraction would make any number of scenarios possible around pre-mining tx validation. The only thing you can really do right now is implement this via a proxy-contract that executes a function only if your minimum time is hit. Of course you'll still be charged the gas if the tx is mined.
It's not very scalable but the Parity node wallet allows you to specify a time in the future to submit a transaction (select 'advanced sending options' when making a transaction). Of course you need your Parity node to be running at that time so you may need to consider hosting it on a server.