Sounds like a fun day. BX can be tough, and getting blown out in the first round is a bummer. My son did a USASA skiercross last year and got beat pretty bad too.
If you didn't already buy him armor, I would not recommend either of the ones you put up above. Get him a full jacket like
http://www.backcountry.com/store/POC...so-Jacket.html
It doesn't have to be POC, most any brand that fits him and is comfortable will do just fine for him. I have a Dainese one that I like, but those are spendy like the POC stuff. I think 661 and Skeletools and some other companies sell similar stuff for less money. A full face helmet would be a good idea too, if he likes his looks.
Learning to double jumps is important, as well as riding a flat board fast. He may find it easier if he mounts his board with a much more forward stance than he's probably got now. I'm not a good example because I ride with hard boots and very steep angles, but I'd suggest doing something like +10-15 rear and +14-20 front. Being oriented more toward the tip of the board will help him set up for turns and carve better. If he rides switch at all in a BX, its only because he got spun and he'll just turn himself around quickly so the forward stance won't matter there. It will also decrease his heelside blind spot, which could be critical in avoiding a collision.
The most important part of a BX is the first 5-10 seconds. Have him practice pulling out of the start and accelerating as fast as possible toward the first turn/feature. If he can win the hole-shot, he'll be in great position to do well. Also teach him that he is faster on the snow than in the air. He needs to clear the jumps so he lands on the down-slope, but on big rollers, he wants to minimize his air time. Absorb the bumps as best you can and accelerate down the back side. Good wax and if its sticky/wet, good structure to the base can really help too. Edges matter when you are trying to carve a turn in the later rounds. Teach him to keep his eyes up and ahead. He should be focused on the next two turns/features, not the one he's on (its too late to do anything about that one). Looking ahead will slow down the feel of the course and give him time to set up. Also, remember to look where you want to go, not at the thing/person/rut/gate you want to avoid. If he wants to carve a turn really close to a gate, look at the spot on the snow right next to it, not at the gate - stare at the gate and you'll hit it and maybe dq.
If your terrain park has some big jumps, he can use the landing ramps as good practice areas. Get up some speed, and rather than hitting the big lip of the jump, bypass the lip and just air as you roll over onto the landing area. Try to pre-jump the drop off so you fly close to the snow and land as early as possible. Absorb the landing with your knees and accelerate - speed checking (skidding sideways momentarily to scrub speed) is for the entrance to the jump if necessary - not for the landing where you are way more likely to catch and edge and get slammed. On the day of the comp, be sure to get there early so you can try to run the course at full speed a few times in addition to previewing it. Practice the doubles (two rollers following one another in quick succession) and determine if he can carry enough speed to carry the gap. If not, work on pre-jumping the rollers and just pumping through them. The worst feeling is coming up short on a double and casing the lip or worse, the front side of the second bump.
Remember that it is HIS race. He only needs to worry about the other kids when he is trying to set up to pass them. If they are behind him, they don't matter - try to tune them out. If they try to push him in a turn, he should do his best to hold his ground, but not push back (it is against the rules, plus it will take his balance away if the other kid goes flying).
Enjoy.
