It's fine for all categories except Any% (with wrong warp). You just have to mark your runs as emulator runs.

Your best bet on the Wii would be to run virtual console. I haven't tested it myself, but I bet that running an unofficial emulator on Wii will produce a lot more input lag than VC or even just running an emulator on PC. All-Stars is far slower than VC due mostly to all the extra animations.

Clips can happen when you jump into a corner in such a way that your pixel and subpixel values are high enough for the game to push you to the right instead of the left. All you have to do it jump at the corner, and if you hit the right pixel you have about a 50/50 chance of getting the clip. P speed can make this easier, but it's not necessary. 7-1 clip doesn't use P speed, for example.

To keep P speed after exiting a pipe, you have to enter the pipe "cleanly". For vertical pipes hanging from above, you just have to jump into the pipe with P speed. For vertical pipes coming out of the ground, you have to jump onto the pipe with P speed and hold down to enter as soon as you land on the pipe without taking a step on top. For horizontal pipes on the ground, you have to jump into the pipe rather than running into it. If you entered the pipe cleanly, you will have plenty of time to react and jump off of the pipe to keep P speed. In some cases (for example, the pipes in 5-Tower) it helps to take a step before jumping off of the exit pipe.

If you have any other questions or just want to discuss running SMB3 in general, come join our Discord server: https://discord.gg/np3WWXR

Unfortunately, VC version works a little bit too well with the wrong warp, as it sometimes produces a successful ending when the original NES version crashes. This is why wrong warp speedruns on VC version are not accepted.

Since you mentioned it, PRG1 plays exactly the same as PRG0. In fact, the aesthetic changes are the only differences between both versions.

Good news! I found a leaderboard on another website, called Twin Galaxies, whose rules seem to be in line with what you are requesting. You should check it out, I'm sure you'd fit in perfectly.

http://www.twingalaxies.com/game_detail.php?gameid=413&platformid=23

The intentions of the game developers are impossible to discern without asking them directly or referencing official documentation. As has already been pointed out, wall jumps, zips, and even 3rd door are all SUPPORTED by official documentation. If developer intent is your justification for banning these techniques, then you have even less of a leg to stand on than most people do when they claim developer intent in other cases.

To your other points:

Improper directional use of a programmed transportation device (ie: Wrong way warp, and DKC2 Expired Time Barrel Glitch) -- This is already banned in all categories except Any%.

Passing through or exploiting solid walls (Wall glitching (SMB3 & SM64) -- I've already addressed this in my first post.

Wall Jumping or Area Skips, with exceptions to intended invisible walls ie: DKC and Super Metroid) -- Again, this is an INTENDED MECHANIC ACCORDING TO NINTENDO THEMSELVES.

Cartridge or system errors, sometimes occurring with equipment failure (ie: visual errors/ screen distortion) / No cheat codes or cheat menus (through unlocks or pre-programmed special codes) / No Game Genies, Gamesharks, or Code Alertering devices that can interfere with the game's original programming. / Any other code breaking method to unfairly advance your progress in the game not as originally intended for progression by the original programming of the game. -- These are already banned in all categories. Also, you should examine precisely what you mean by "unfairly advance your progress". Unfair to whom? In what way?

One more note on developer intentions. Regardless of what the developers intended, there are no video game police patrolling the streets and looking for dirty, stinking cheaters who don't play the game exactly the way it's supposed to be played. The closest thing we have to that is moderators on websites like this. If you spend time participating in the community (do more runs, hang out in other runners' streams, join the discord server, etc.) you might find that the moderation for SMB3 at least is mostly a reflection of the SMB3 community as a whole. If and when there is a significant and ongoing demand for glitchless categories on the main leaderboards, the community as a whole will decide whether or not to add them.

The No Wrong Warp category excludes one major glitch that completely changes the run. A run that includes the wrong warp is fundamentally different from a run that excludes it. That is why we have a category that bans just the wrong warp.

"Sketchy" is subjective, and if you discuss this with the rest of the community you'll find that almost no one else shares your reluctance. You'll need a stronger foundation for your arguments than sketchiness if you want to make any headway.

Repeatedly characterizing tricks you personally don't like as "cheating" when the consensus within the community is that they are fine won't get many people on your side either.

Hypothetically, if we were to add "No Glitching" categories to SMB3, we would need to define very specifically what is or is not a glitch. As it stands, besides the wrong warp, glitches in this speedrun by the most liberal definition really only include zips and wall jumps, and both of those are debatable.

Zips are a natural consequence of how the game handles Mario getting stuck, for example, while un-ducking under a block. The game always pushes Mario to the right when his head is inside of something. Should we ban runs where a runner inadvertently un-ducks while ducking through a one-tile gap? If not, how do we differentiate between intentional and unintentional un-ducking? If we should ban zipping in certain locations, what's the justification for saying you can let the game zip you out of a wall here but not there? Considering the zip using the 1-up block in Bowser's Castle is mentioned specifically in Nintendo's official strategy guide, can you say that something intentionally left in the game with purpose is a glitch per se? In any case, the effect that zips have on the speedrun are minimal, and a separate category disallowing them would result in having two near-identical speedruns with only one miniscule difference between them. To what end? So that a handful of runners can feel good about not "cheating" according to an arbitrary rule that the vast majority of the runners find pointless?

More to the point, making these official categories is not something you will accomplish on your own; you'll need to convince the community at-large. Your best bet is to codify a set of very specific rules governing what is and isn't allowed, continue to run your category to build recognition of it, and convince other runners to do the same until it becomes ubiquitous over an extended period of time. I can tell you right now that that last point will likely be your undoing, as there are plenty of other, more unique runs with lots of supporters that are also left off of the main leaderboards. I'm not trying to discourage you--you have my full support in doing whatever makes you happy--I just want to make sure that you don't half-ass something you feel strongly about.

There's not much to the clips. For the corner clips, just get a running start and duck jump, aiming for the ceiling about half a tile before the corner. For the 1-up clip, just trigger the block then duck jump around and onto the block.