Personally speaking, I would prefer if Barik had tinkering as his base weapon, and replace tinkering with hair trigger. I really don't think that a point tank should potentially have a dps of over 1,000. I'm fine with him damaging more than other point tanks and being more mobile, especially since his mobility and damage is his sustain to a certain extent. Like, here's the changes I would make:

base weapon: dps of 500, a single blunder shot with the damage being fully effective up until 75 units, with gradual falloff and have his max damage reduced by 50%

buff his healing/shield cards on rocket boots. Like I would buff Bowling Ball to {200|200} and Double Time to {65|65}

I agree with your hp increase. I'm neutral about the turret talent getting buffed, it's not going to be much extra damage if I'm being honest. I agree with the shield cooldown, I;m neutral about the the bunker card, since it wouldn't make much of a difference if I'm being honest; that's like 250 extra shielding, in a meta where shield wreckers should as Vivian and Viktor dominate.

I don't agree with your assessment at the bottom. The problem is that instead of being a point tank, he's a pseudo dps. It could carry games and he was downright broken when he had the crazy sustain on top of the crazy damage, but now that he doesn't have the sustain anymore, he's just not as good. Especially in the sustainy hitscan meta where he can't sustain against hitscans or outdps their sustain. I'd rather more sustain and less dps for a point tank, than the other way around. I do think he should ultimately have more damage than Inara and Terminus, along with more mobility. He shouldn't have damage reduction, but he should have self-sustain options. I don't want him to be an Inara, no one wants that. At the same time, he should still have some sustain as a point tank.