Should I wait to submit an award for more bullets and a higher commendation?

Depends really on how much impact your Battalion Command Team thinks that Soldiers contribution was. Generally when they feel it's that type of impact to warrant an award higher than an AAM they usually are the ones beating up the company leadership to get it written up and sent up. More times than not they don't know the small victories and it's up to leaders like yourself to send it up. I recommend discussing this with your company CDR/1SG to get their feel of it and quickly because it sounds like they're closing down soon and chances are your soldier will never see that award because of deactivation. 

SGT H, give a Impact AAM, I am sure he has done other things and will do more during deactiving to get another/higher award.

I personally wouldn't wait. All too often soldiers do not get recognized for the great individual work they do because of the 'he's already got x amount' rationality.  Remember that as he grows up, it's not just appearances of medals on his chest, but what each medal was awarded for. There is the possibility you leave, he gets tranfered to another squad, section, etc... and this opportunity for him is just another blip on the radar for someone else to not deem worthy. Award the guy for his job well done and let the PCS/ETS award write itself for higher commendation by actions he has done throughout his time there.

In relationship to other comments, points for promotion is the very last reason a soldier should not be recognized. It is not my place to say whether or not this task deserves an award or not, but you as the recommender seem to deem it worthy and that's all that matters. Remembering that a soldiers career does not end after promotion to E5/E6 and that his entire board file for E7 and higher need to reflect his ability to perform ahead of his peers. Each and every little thing contributes to that.  It is up to the task completed to duty description for the command group to approve an award. You write it well enough, and they will have no choice but to approve it if it's deemed appropriate.