I HIGHLY suggest you come to terms with the fact that you don't make the rules here. If you want to regain your medical certificate, you're going to have to stop trying to find ways to manipulate the outcome in your favor, accept the rules of the issuing authority, and decide that you're going to play by their rules. Otherwise, as Dr Bruce would say, you're going to end up taking the bus.
Just a couple thoughts:
There are 2 different reports to the FAA. OP should read these carefully and get professional counsel as appropriate. Midwest Flyer has a nice write-up
here.
The first,
14 C.F.R. § 61.15(e) (Details
here) which seems to apply to all pilots (with any certificate type or medical type) whether active or not: "requires all Part 61 certificate holders to send a written report to the FAA within 60 calendar days of any drug- and/or alcohol-related MVA". MVA is defined in this section and is not the same as your states definition.
I have seen that this is not required under BasicMed though I can't find it in the regulation, Anybody have a citation?
This report is not automatically required based on an arrest and it can possibly be required twice based on some interim actions the enforcers take. (it applies after convictions but also some other actions like any suspensions) Read and understand it well.
This report goes to the agency's Security and Hazardous Materials Safety Office, Regulatory Investigations Division and may result in action against the Pilot certificates, not the medical. That said, they also usually send notification to FAA's medical who can and usually do take action against a current medical. If a medical is not required, is expired, or otherwise not actionable not much can be done though they might do something not in the regulations anyways.
If you have a class 3 AND BasicMed they can withdraw your Class 3 medical and BasicMed is invalid. This process is very slow and I know people who didn't get a letter for over a year, a Class 3 may expire.
The second report is when you apply for a new medical, It is a reportable event. If you don't apply, then it is N/A and your medical expires. Most would argue you know at that point you no longer meet the requirement for the class 3 without an SI and must ground yourself. There is no regulatory requirement for a report here, though many do to get the SI process rolling. Unless you want it to just expire.
As far as BasicMed, as WDD posted: "Substance dependence within the previous two years, as defined in
14 C.F.R. § 67.307(a)(4)" is disqualifying. First, this is a 2-year rule so it's possible to wait it out.
Note well: The FAA's definition of "dependance" is quite different than what your real doc might use in determining your suitability to fly.
As mentioned, if this applies, read these regulations carefully and get professional counsel as appropriate. You want a real lawyer to manage the DUI and an Aviation Lawyer and an AME to manage the FAA stuff. It's a regulatory morass and what's useful in the courtroom might be a mine-field in the other. Posts on POA are interesting, but you likely want a pro to help.