A few points
“(29 days, 12 hours, 793 chalakim)/2 from the previous Molad.”
This isnt according to all. The Mechaber says 16 days. The MAgen Avraham understands this to mean you have until the end of the 16th day. The MB understands this to mean meis leis ie 16 x 24 hours from the molad.
Iacrisma is right according to Ashkenazim, as the Remah says it is half of 29 12 793.
“Follow up: Also don’t forget to add an hour during the summer when the clocks are an hour ahead.”
A more important follow up is correcting for where you live.
The molad isnt based on the time that you see on a clock. It is an average molad taken by adding 29 days 12 hrs and 793 chelakim to the previous molad.
The time that is announced in shul is the time that this molad occurs in Yerushalyim real time. today we use standard time. Ie a chunk of the globe ~1/24 the circumfrence all has the same time. In Yerushalyim the molad occured as Iacrisma said “The Molad for Tamuz was Wednesday evening 5 minutes and 7 chalakim after 6. ”
If you were in Yerusahlyim and checked the time on your clock that the molad occured. Your clock read 5:44 and 7 chelakim (Israel standard time is 21 minutes earlier than natural time) due to DST this is 6:44 and 7 chelakim.
In N.Y. which is 7 hours “behind” Yerushalyim, the molad occured when the clock read 11:44 and 7 chalkim on Wednesday morning. Thus there is even less time than iacrisma indicated if you are west of Israel .
(Rabbi Heber argues that leap seconds should be subtraccted as well, though that obviously has little, if any, practical significance)