Testosterone decreases but it is within 10% of the peak throughout the day.
So if in the morning you test at 600 ng/dl, your levels will stay above 550 the remainder of the day.
I personally don't think it matters what time of the day you do your TT test or your E2. The only thing you really need to do in the morning on a fast in regards to hormones is IGF-1.
Your FT is higher in the morning, this would lead me to believe E rises throughout the day, since E has a very strong correlation with SHBG. Meaning as the day goes on your SHBG rises, which reduces your FT level, if this is the case, E will surely rise with SHBG.
Hope this helps