Negligent is really going to hurt. Same as Reckless etc.
All Trucking Companies that have a DOT/MC number generally are going to run with the same challenges against someone who might have something like that stamped on their Driving Record by the home state. Suspensions is a whole another set of problems and indicates things are not well.
That I think combined with 10,000 other billy bobs wanting the same job you are applying for anywhere in trucking that hold clean DMV's and so forth are going to get hired before you.
There are tiny opportunities to run yard dog or something totally off road, as in on private company property, you don't need any kind of licensing at all to do that with a 18 wheeler. Just cannot put a wheel anywhere onto a public road at all. (Or outside the company gate)
Ultimately its the Company Insurance that decides if you are hireable or not depending on what you present with the DMV. They use that as a first filter to weed out problems like what you have listed so far.
I am not trying to be difficult or be a opponent. There was a time early in my Class A (Prior to CDL days) that my record was not that great. (Tickets by the stack) and ultimately took 3 to 4 years to cool all of them off. A judge did specifically enjoin the state not to automatically suspend me on points accumulation in those days. That's was how bad it was then.
Today's trucking with what I really consider extreme rules and regulations among other things behind the scenes, a little tiny whoospie or violation can destroy a trucker relatively easily.