With regard to wearing a tie, I once asked one of my Rebbeim if I were to dress for davening the way I would dress in front of a king or president, logic would dictate that I should wear a suit and tie and then there would be no difference between davening and Shabbos. He suggested that it meant if you were standing in front of a king that you see multiple times a day like if you were working for him. In this day and age, it would mean no jacket and tie but he still suggested to wear a jacket so that something special is worn specifically for davening.
With regard to the hat and JFK, it may have been true at the time that hats were still respectable and he was lowering the bar for when to dress respectfully but that’s certainly not true anymore. Now a hat is simply not respectable. Even if a real king would exist, a vast majority of people would not wear hats as it’s no longer respectable and might even look a bit ridiculous. JFK may have started it but the transformation is now complete. Styles and respectability change. What was respectable in Rashis time in place was not the same as the Shulchan Aruch which wasn’t the same as the GRA which isn’t the same for us. The stylistic reality is, is that hats are out.
With regard to one hand out of the sleeve, I think Rav Soloveichik held that way. At one point later in life he stopped wearing a jacket for Shacharis. He explained because he just inherited R’ Chaim’s tefilin which were quite large and couldn’t fit under his jacket sleeve. He felt it was more respectable to not wear a jacket than to wear one abnormally with one hand out of the sleeve.