Why exactly did the new job not hire you? You should be entitled to a copy of the background check/other info used in the hiring decision. Unless that's just a California/state level law that's not applicable to Texas. But I do believe it's federal. Same with the credit check if that was a part of the background.
I'm headed in this direction due to the fact that you have a FTA/bench arrest warrant you didn't know about. Not sure how that reads on a non law enforcement background check, but nobody is going to hire someone with an open arrest warrant so that's likely the reason you were unexpectedly denied. That's explainable IMO, especially after being honest about everything else. So you might be hireable if you take care of it.
At this point it can't hurt to ask. They've already invested significant $ in you through the hiring process, drug test, background check, time, etc, and they were seemingly ok with the stuff that you were upfront with them about from the start, so maybe this is a fixable hiccup.
At the very least you get a free copy of your background check & other info that was used against you. This can help you be "more honest" with future employment opportunities as you'll know exactly what they'll see and what you might need to discuss/disclose going forward.
And yes. Use every resource available to you through the VA. Check out USAA for car insurance if you haven't already. They were the cheapest option for me. Make sure you're legal BEFORE that though. For being supposedly veteran/possibly bad situation friendly on the outside, they also have ZERO issues with being judgemental ****** at the first sign of trouble & their "standards" seem to bounce all over the place. I had some trouble years ago and filed bankruptcy, leaving them with a fairly hefty write off. I've been in their "doghouse" ever since: kept home/auto & bank accounts but they shut down all access except for the mobile website & app. Other's have filed bankruptcy and had all accounts cancelled/non renewed even though USAA carried zero debt. Fairly crappy treatment, but they're still they're still the cheapest option for me. Ymmv.