I agree with everything LuckyCat said, a couple of other points.
First, if your son wants to stay local, then no need to go to a national recruiting showcase at all, stick with PBR or other local ones. When you go to a showcase, you will be seen by schools you have never heard of, but it's still better to write to schools that are of interest, tell them about yourself, give them your summer schedule, and ask them where they will be able to see you (they may just say "come to our camp" which doesn't mean much).
In answer to your timing question, the most academically selective schools are working backwards from the Early Decision application deadline in early November. If those are your targets, and you are hoping to get admissions support, then many decisions are taken after the August Headfirst/Showball showcases. Yes, for those schools, the September/October showcases senior year are probably too late - but, schools whose top choices decide to go elsewhere may still be looking to fill slots in October. On the other hand, if you are looking at schools where your son would probably be admitted without support (and many of those schools are also at Headfirst/Showball), then the whole schedule is more relaxed.
Partly it depends what else your son is doing for recruitment, and what his skill level (measurables) and academics are, and that pitchers are different from position players. If he's playing high-level travel ball in major tournaments, then contacting target schools individually with his schedule will get HA D1 eyes on him, as will having his travel coaches contact schools, or attending individual camps. If he's a position player who has the skills for D1 schools, then a HA showcase in the fall of junior year is a good idea. If he's a D3 player, then plan on showcases in the summer before senior year; if his numbers stand out (i.e. has a very strong 60-time, inf velo, exit velo, pop time, fastball), then one showcase may be enough, if he needs to be seen playing (because his numbers don't stand out), then maybe more than one.
In addition to Headfirst, Showball, and Stanford, the other major academic showcase is Arizona Fall Classic in October.