As a mechanical engineer, I tend (as do many others even non-engineers) to default to purely mechanical assessment of the problem... e.g. the geometry of lungs, tongue, mouth, head, body, MPC, horn...
But it should probably be approached more as: three more or less equal parts, mechanical, physiological (e.g. a Dr./Dentist/Orthodontist assessment), and ultimately an artistic assessment... listening and feeling (physically and spiritually).
That said, I've found that issues at the front of my oral cavity and with its shape have a great impact on the rear of it. So, yes, some effect on articulation is likely to be present, but also note whether there is a conflict between tip of tongue being able to freely articulate, and rear of tongue impeding throat opening and airstream... that's been my issue since I was a 12-year-old student, though I only realized it 50 years later, through the 3-part analysis mentioned above.
Whether you have issues to the rear of the oral cavity, and, if so, how to deal with those fore and aft issues, or just the tip of your tongue if that is all, will require individualized study, adaptation, and perhaps therapeutic means, e.g. orthodontia, breathing exercises, tongue muscle development for adaptation, etc.
In my case, I have neither under- nor overbite, but I realized early on that clean articulation of more difficult passages, esp. in the low register, was difficult, and that my airstream was a problem there. Tonguing always made me feel as though my throat was closing off, a big problem.
It was much later that I realized that my jaw/teeth shape, particularly at the sides, was a huge aggravating factor. Until then, it felt as though my tongue was too long, such that, when tonguing, it would close off my throat, in the same way that some people cannot pronounce "L", getting more of a "G" sound... not a problem for me in speaking, but very much so with the MPC in my mouth. I then learned that my teeth do not form a wide "U" shape, which I think would be ideal, but rather a "U" with the sides pressed in and a more pointed shape at the bottom. I think this can be caused by thumb-sucking, but I've learned that mouth-breathing can be a major contributor. I was a mouth-breather as a child, and I think also as an adult, while sleeping, until I got a CPAP machine with nose-only mask.
Anyway, the narrowness of my oral cavity has, I'm convinced, been my problem, rather than a "too long" tongue.
Thus, your underbite may or may not be your only problem, and it may not be much of a problem at all.
Bottom line: You may (and probably do) have more than one issue, and should consult with a professional. I would start with an orthodontist. But there may be alternatives to their solution... think outside the box and you may come up with breath work, tonguing exercises, who knows... yoga? Everyone is different physically, and has resuliting limitations. Many of the greatest players have overcome theirs with simple study, analysis, practice, practice, practice, and adaptation. Did I mention practice?
All the best in overcoming any issues.
PS: Angle of MPC to mouth is important, and is also a very individual thing. My gut says that your optimum may be a more upward angle. But in any case, a sufficiently tight neck strap, on anything other than soprano, is critical for all players, and often neglected. This allows you to maintain alignment of your head/neck/body, with resultant optimum air column. Getting that right with a more extreme MPC to mouth angle may be a challenge, but is worth attaining.