I'm a little confused: you say "In Jerusalem I attended a Jewish church service." Were they Jewish Christians, Jewish Meshiachim (Messianics), or a mixed Messianic congregation?
At any rate, the society you were part of sounds interesting. The Rabbi you mention is following a Talmudic/Rabbinical form of Judaism. He is likely bound by the 613 mitzvoth; those "laws" people like to throw out at Messianics. First off, Torah is usually more accurately translated as "instructions." And second, while based on Torah they are found in the Gemara not as a list but as many halachic rulings over many years by various rabbis. As I said earlier, we do not consider ourselves bound by those rulings. I do look at them and try to understand the reasoning, as these were godly men. But I do not always agree, and never blindly follow.
We too typically blow the shofar to begin our service. It is how the ancient Hebrews were called to service, to meetings, or to arms. For us it is a clear signal it is time to shut up, get to our seats, and prepare for worship. Much more effective than a deacon standing up front saying "Can I have your attention; we all need to be seated; it's time to start." ... "Please, can I have your attention ... !" I will admit, though, that being inexperienced at it we sometimes sound more like slaughtering goats than a call to worship. Still, it will get your attention!