I really appreciate your paper on “lip flesh” (abbreviated term) for I, when
young and inexperienced, was a victim of the one way and one size fits all
syndrome. On a scale of 1 to 10, with 10 being very fleshy, I would rate
myself as 7/8 and tend to bottom out on very shallow mouthpieces though I
like the shallow for when I need play lead or extended periods. I have
also determined that I have not figured out how to determine throat size.  I
have tried some pieces with small volume cups and small throat that seemed
to blow easy, though I bottomed out, and also large cups with large throat
that seemed to blow easy as well.  So maybe it’s the entrance to the throat
that determines that more so than the throat size itself???

Doctor Mouthpiece:

This is a great question. I have to note, right off, that you equate shallow cups with small throats (what we call the bore size) and indeed this is usually what is presented in standard stock mouthpieces. However, each of these elements plays a critical role in its own right and should be manipulated as needed, accordingly.

The bore is a major regulator of air flow. Opening or closing the entrance to the bore is really an extension of cup volume, but the actual bore size is “the keeper of the keys” as it were. This is easily illustrated by going back to my old analogy of the garden hose. Remember, what you do before the bore (or on the feed end of the hose) is still primarily governed by the hose itself. A chink in the hose still closes things down.

Bore size combined with cup volume are primarily responsible for The Internal Volume Equation (IVE) that we look most closely at when fitting a player. Every player has a Personal Velocity Parameter. This means that every player has a personal threshold of how much air they are capable of moving to velocity based on their individual physiology. In your case, your fleshy lips dictate that you cannot use extremely shallow cups. This means that your IVE is alreadygoing to be significantly larger than someone who can make use of shallow cups. You say,  “I have tried some pieces with small volume cups and small throat that seemed to blow easy, though I bottomed out, and also large cups with large throat that seemed to blow easy as well.” While, I don’t mean to dispute your personal experience, I do think it’s important to qualify this experience. If “blowing easy” was the only criteria we need to be concerned about, indeed the range of successful mouthpieces would be much greater. However, not just blowing easily, but rather the results we get when we blow need to be taken into careful consideration. This is where the PVP (personal velocity parameter) factor really kicks in. If a player is attempting to use a mouthpiece with an IVE rating that is simply too high for hisPVP, (did you get all that!!??) maximum velocity will not be achievable by the player and performance results, on many levels, will break down. Again, this is not the sort of thing that you may notice when playing very simple material, but once you start to ratchet up the difficulty level, the differences will become painfully obvious. Having worked with so many of the world’s greatest players, I’ve been able to see quite clearly that, as the claim goes, these people can play on anything…if they’re playing fairly simple stuff. But, turn the heat on and they become extremely picky about what they will use. If this weren’t the case, these people would happily change mouthpieces all the time…but they don’t! They generally have 2 – 3 pieces that they use for specific applications…as should be the case. Finding and critically placing maximum internal volume in the mouthpiece for a given player’s velocity threshold is what it all comes down to. In your case, the simple answer is to go only as deep as you need to in order to keep from bottoming out, but at the same time to tighten up all the other factors such as bore, and back bore which will help to bring your IVE back to manageable levels. We can even adapt the cup shape in a way that will accommodate your fleshy lips where they are apt to touch, but scale back on the rest to further reduce the IVE.
Once both the IVE and the PVP are in balance, dramatic and striking changes can occur concerning the playing technique. Even though the variables at play are myriad, the end results are always the same; a dynamic improvement in all areas of playing. Things that you had always been told should happen (and never did) actually begin to occur…easily. It really is all about the air. Freeing the player to release the air is the key.