Hey bro, my gf has has hashimoto and i've learned some things about T4, first things first i think you're jumping on a too big of a dose. I know some guys start with 50mcg. Maybe that's not much but straight to 150 seems a bit excessive, especially if you're still in the reference range.
What time of the day you take it doesn't matter much, although is recommended first thing in the morning because you need to be on a empty stomach and wait half hour before you eat. Also as you mentioned taking it noon-night might interrupt with your sleep so better not risk it.
I'd suggest to pay attention on the consistency of your timing though, because that matters much. If you take it every day lets say the exact same hour or a little +- it'll be perfect. Taking it one day at 6 in the morning and following days at 10 or 12 is not advised.
Yeah i'd start with 500. Usually bros taking the XR because they take it all before bed without berberine in the day, i think from the time you'd supplement with berberine 1-2 times within the day even the non XR version would work well. Cheers brother!