The latest appointment time the lab offers would likely give oyu the lowest T value.
Keep in mind that the time of the test is indicated on your labwork, so unless your doc is an idiot (quite possible), then they're not likely to fall for it.
Methods you can use to temporarily lower your T value were written in an article on here called "Your Doctor Your Dealer". You can probably search and find it.
Methods included: getting shitfaced before your test. Not sleeping for a day prior. Eating soy.