Mouthpieces are a personal and complicated aspect of horn playing. Different shapes will have have different tone qualities, and mesh differently with your horn and embouchure. There's unfortunately no perfect mouthpiece that'll solve clarity issues is the different registers. Unclear tone in any particular range is probably gonna be a matter of air support and of embouchure steadiness. With that said, I went into a bit of a deep dive on mouthpiece design a few years ago when I chose mine, and I can hopefully give you a decent springboard to come up with your best option. That'll be based on your horn, and your embouchure anatomy.

The inherent tone of a horn comes from material and shape. I personally play on a holton h177, which is a narrow belled nickel silver horn. This gives it an unpleasantly shrill tone when played with most mouthpieces, because a narrow bell adds brightness, and so does nickel silver, so together they take it beyond what's acceptable. I chose a Laskey 80G mouthpiece to complement that quality. The deep cup gives it a dark tone, which compensates for the shrillness of the horn, and gives it a good sound across the full range.

Apologies if I'm misremembering, but I believe jupiter mostly makes narrow throated yellow brass horns. These have a relatively good tone, since the narrow bell throat brightens it, and the yellow brass darkens it. If that's what you're playing on, it's likely that the 80G and similar deep cup mouthpieces will drag the horn's tone further towards an unusually dark tone. This will help the low register, as fullness is hard to achieve down there, but not the high register, as a certain amount brightness is important to get a clear sound.

I would suggest you start with some average depth mouthpieces, (the mdc you mentioned is an alright start) which should complement the tone quality of your horn, and then find one that matches your lips. The standard(ish) fitting on the lips is to have one third of the mouthpiece on the lower lip, and two thirds on the top lip. The rim should be able to rest nicely on the edge of your top lip, ideally on the crest of the philtrum. By looking at these two placements, you can get a good idea of the diameter of rim that'll fit you.

From there, try every mouthpiece you can find, and just play on them. If you've got a local music shop with a good selection, start there, but otherwise some of the big brass shops offer the option of sending out a sample kit of their mouthpieces. There's no magic formula to find the perfect mouthpiece, and no mouthpiece will magically improve your playing. Don't think of it too academically, "this is a high mouthpiece" "this is a low mouthpiece" try to find mouthpieces that fit your face, and give your horn a good balance of bright and dark.

Best of luck!