These guys are right about it being easiest to go in the morning if you are fasting.
I don't know if it really makes much sense to go later in the day to just get a lower T reading. The results will likely have the time printed on them. Any doc who really knows TRT is going to know that your levels drop through the day. If you are seeing someone who is ignorant enough to be fooled by it, then you aren't seeing a TRT expert.
There is, however, something else you can do: do not sleep at all the night before the test. Just make sure you think this through and consider your future testing and plans before you decide to go through with it.