Should we prioritize having a more broad set of neutral defensive interactions, or a more narrowed selection of key resistances? If we choose to narrow our defensive options, what sort of critical interactions should we try to work toward or avoid?
I'm not sold on one over the other. A generalized defensive presence feels like it'd end up as a workable but not very convincing wall. I'm reminded of like Gastrodon, the stats are good for being a wall, you have recovery and utility moves, and your Water/Ground typing is hard to exploit while having useful properties like an Electric Immunity and either a Water immunity or security versus Trick and Knock Off depending on if you run Storm Drain or Sticky Hold. In spite of that, you aren't resisting enough of the big offensive types to really work, nor is anything you offer terribly unique or worth overcoming the disadvantages for.
At the same time a narrower approach is going to be more dependent on metagame factors to find success than a broader one. If we identify Sun teams as something that needs a better defensive answer, this CAP may not be able to survive in a metagame where Sun is suddenly absent.
I feel like we need to be, specifically strong versus a broad set of Pokemon? This sounds contradictory but what I mean is, a physical wall that is resilient to passive damage, or a Special wall that excels versus any Special booster. We need to approach this with "what exactly are we trying to wall" in mind and going in with a generally good defensive suite might just flop if it's not providing the team with anything it specifically needs, or if our specific defensive capabilities are simply too narrow to help when the opponent doesn't have anything this CAP is useful against. In the former two cases, we're looking to be strong on one side of the defensive spectrum, but targeting a specific subset of Pokemon in that spectrum we are equipped to handle. It doesn't mean we only handle those Pokemon, but that we offer an surefire answer to them that teams will want, and come packaged with any other winning matchups by default. You'll often add Arghonaut to a team because Unaware is massive versus setup users, and in doing so you've also given your team a Dark, Water and Fire resist that's just useful in general.
I'm not sure how much this really answers the questions you have: it's hard to talk about how we operate when we only know how we're supposed to with zero other contextual material to work with, and the above was mostly just braindumping that uncertainty on my end. Overall I feel a general approach should be cautious to not be "too general" and fail to actually address anything people use in CAP. Narrower approaches conversely need to be capable of doing more than just one or two specific duties that may only function if the opponent loads the right team, else they end up dead weight.
Are less-defensively potent typings that place more emphasis on limited offensive interaction desirable? If so, where should we be aiming to draw the line between our offensive and defensive profile?
I find that we should avoid trying to be "cute" about the concept with the notion of offensive capabilities being a useful defensive property. Threatening specific Pokemon is a nice trait, but not necessary nor even desirable for many walls to function. Our focus on our chosen typing shouldn't be a result of having STAB into common threats, but keeping us safe from common attacks and coverage combos. I don't feel we need our typing to be the cornerstone of our offensive capabilities, as many walls often forgo STAB in favor of moves which better play into its strengths or versus the mons it wants to check or try to check it. Corviknight, Ferrothorn, Toxapex, Dondozo, Mega Latias, and Dragonite have run defensive sets without any STAB moves at some point, or even regularly, though many of them have the stats, typing, and moves to do so. Their attacking moves of choice are usually those that match up better into the metagame, against the Pokemon they are often pitted against, or simply synergize better with their strategy (Body Press is notable here since it gets stronger off of Defense investment instead of Attack).
Point being, I think offensive angles should be opportunistic in nature rather than a driving force of our strategy being a wall. If we're fully capable of serving as a wall, we should have the moveslots available, and the turns generated from our longevity to give us enough room to start dealing damage. Being faster than the average wall only makes this easier. I'm not saying you can't sell your typing as have useful offensive applications, but that the defensive potential of the typing should be the primary focus and not be compromised on.
TL:DR Let's keep our typing solidly defensive in nature and worry about threatening the opponent offensively when we have a better foundation to work from.
Should we seek typings that can fulfill our defensive needs more or less regardless of how high our Speed ends up being? If not, what sort of typings are more or less potent the higher or lower on the Speed spectrum we find ourselves?
I don't really have a preference for either of the two options. A typing that doesn't need to be fast to work defensively lets us explore what happens when said typing ends up being fast anyway, while a typing that works better the faster we are does more to demonstrate how Speed can be a huge part of what allows a defensive Pokemon to achieve viability even if the typing may seem more vulnerable at a glance.
If we wanted to focus more on the Speed-dependent types, any typing that has serious merit both in offense and defense is going to prefer having higher Speed. Another option would be typings where their commonly run moves can inflict status, or any typing that relies on or simply enjoys status. Being faster lets us spread that status before the opponent acts instead of after, and that's useful for all the non-Poison statuses because it means they can be in effect immediately. Even Poison and Toxic could be helpful if we find ourselves in a losing position where getting one last status off is the best way forward, something other Walls may not be able to accomplish.
and Swampert's 
typing, a lot of resistances but a x4 weakness, as an example, almost an omni-wall, but not completely, these typings would help on the low-end Speed tier, as it is not able to outspeed the faster Pokémon in the tier, so the typing allows it to survive those matchups. If the speed is higher, a less defensive typing would be good, as the Speed ensures the survivability, not the typing. (Not saying it should have an offensive typing, but it shouldn't have a one-weakness only typing, for example).
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