Great Post!
Was excited to see I get a mention in it too!
I've really been enjoying Ballistic since unlocking and using him this past week. Getting good consistent kills with him, a few wins too.
Initially I avoided him because his abilities did not sound too exciting, though I liked the idea of having a third weapon - I considered it would be a 'clutch' weapon to switch to when you and an oppo are dancing reloading in CQC. This proved to become far from how I've used it.
Ulting with Ballistic...
I've found the best time to trigger that Ult is when you see your second teammate engage or about to engage in a push/battle. By this I mean when you know two teammates are about to be engaged in battle - be that you and another, or your two teammates.
I trigger it similarly to when/how I would trigger Bloodhound's ult. It's the kind of "it's on" moment.
Tactical...
I'm not sure how badly this affects opponents as I'm not sure I've experienced it yet, however, it is quite cute and fun - and I actually have several kills with the bullet itself landing.
Hits them for 20-25 damage I believe, and can be good to hit a fleeing enemy or poke a bit of damage in early drop battles.
Because it locks on, it can be a good way for almost guaranteed hit, like as I said, on a fleeing or low health enemy can be really good - and works out well for those early drop low shields spam your weapon cqc fights.
Weapons...
My biggest advice currently would be to consider your sling weapon as your main or secondary weapon. As if you're going to ult to enter a fight you're likely going to be using it more.
Sometimes I've played without touching my secondary weapon.
Usually best to make this a CQC weapon, I've surprisingly enjoyed (and had more success with) the RE45 compared to the Alternator.
So your preferred mid to close range weapon would be a good choice for your main. I'm currently going with the Hemlok. And keeping a CAR or 99 as my secondary for when my ult isn't active.
Seeing as I've noticed you may not need to touch this weapon much, it could potentially be a shout to stack a sniper if you wish, as sometimes you will have a situation it could be handy. But also bear in mind, it can be harder to keep track of three weapons so you may accidentally switch to a sniper in a clutch moment. I have point blank scoped someone before, but definitely would not want this to happen.
I've not been using him long, and I'm by no means a pro. But I've really been enjoying him and these are some initial things I have noticed.