I think Loveshack was recorded with a 12x7 Brady jarrah block snare, it’s definitely going to be loud enough if you go for the right construction.
I took a 12” mapex phantom snare to a rock gig once, at the end of the night I noticed how much it chewed my sticks. Either I was hitting harder to make it sound louder or the position where your stick impacts the rim is harder on sticks (or the rounded black panther hoops) I’m not sure, but I stick to 14’s these days.
I may be wrong here, but when I think of snare diameter, I think more of pitch than I do volume. A 12" will probably cut through a little better and the pitch will be higher than say a 14". More plies does not give a deeper tone. I think it does the opposite.