Personally, I think one rather simple way to do it would be to legalize everything again, but make this rule:
Pikachu and G&W can only fill the bucket with t-jolts, or with 2 t-jolts + 1 thunder (same for other teams - no multi-hit fills). If G&W fills the bucket with a multi-hit fill, he must dump the bucket without hitting an opponent. To dump the bucket he should face offstage with no enemies there (ally could be there I guess...) and clean out the bucket. If he takes a stock with a multi-hit filled bucket, his team forfeits a stock for each stock the opposing team lost [OPTIONAL: but forfeits those stocks after a death unless at one stock at which point they forfeit the game (that is, they forfeit the stock at 0%, since the opponent was OHKO'd)]. If the G&W removes the last remaining stock with a multi-hit-filled bucket, the entire game is forfeited.
Contingency rule - if G&W attempts to dump the bucket at the end of the stage offstage, with no enemies offstage, and an opponent is hit by his/her teammate into the bucket dump and dies, no stock is forfeited.
In practice: Don't fill the bucket with Thunder/multi-hit fills, if you do, just go dump it out. If stupid stuff happens, you probably loe a stock.
This would allow bucketing the way Brawl does (which is actually quite powerful with ZSS), but would stop insta-buckets. And personally, I think if you can fill the bucket with 3 t-jolts, you deserve to be able to use it.
Alternatively, mandating the custom special that instant fills the bucket would be another soluation.
Yeah, I had a feeling that argument would come up. I'd be curious to see how it goes. I'm in no situation to host an event, but I definitely understand that the community has exhausted this issue in previous games. The issue that I see now is that reflectors and counters have been buffed (the most powerful counter in Brawl was x1.2 - Ike, whose counter was slow - and now it's x1.3 - Little Mac, whose counter is very quick), not mentioning custom moves which can push the multiplier to x1.5. New game, possibly new rules? We'll see.
I agree that TA ON makes you have to be much more precise in your teamwork and lessens the 2v1 advantage (which can be arguably unwinnable at fresh stocks). But the game seems designed around TA off and the exploits with TA on feel like they could be metagame defining. Also, TA on promotes 1v1 play to minimize friendly fire, while TA off promotes 2v2 play to maximize lag covering.
https://www.youtube.com/watch?v=zmxNQF-Gzkk - Here's a video I found of some tournament melee doubles. It's a lot of 1v1 with a lot of "help me out" play, which I'm not all that excited about. Any coordinated attacks are usually sandwiching (36:01). Mind you, I didn't watch the whole thing... so I could be getting a completely wrong impression of competitive doubles.
Side note: some characters can still save your teammate during recoveries, which makes them all the more important as doubles partners (G&W... again, Mega Man, Pacman)
Extra side note: Do you play doubles? I've been trying to find doubles matches with my teammate, but finding a doubles match here is like finding water in a desert.
Brawl doubles are a better example - Melee has enough crazy crap that you don't want to be in the way of a Fox waveshine usmashing someone. But with team attack off, P1 grab -> Ike (P2) fsmash is a thing, and rather obnoxious honestly. There are other rather stupid combos that become much easier with team attack off (Kirby uthrow -> DJ Pikachu Thunder can almost instant KO, but with team attack on precise spacing is required to not only hit and kill your ally - not at all the case with team attack off).
Pairs of 1v1s can also be strategic - they can limit team combos for slow characters but not fast characters, being especially strategic for Melee Fox (Ex: a Samus Puff team can do nasty things to double Fox when they are close, but if the Fox players camp to make them 1v1s, they can fight in relatively strong MUs alone, but with their speed can easily get a hit confirm or make an assist), they can allow exploiting certain MUs in doubles (Ex: I was playing Pikachu in one round and my opponents had a Snake on the team - my teammate worked to engage the other character (Ike) as often as possible so I could be free to focus-fire Snake, get a few CGs, and lay on lots of percent), and can make gimping easier (same example: my opponent being assaulted by my teammate Kirby allowed my Pikachu to focus on gimping Snake instead of having to gimp Snake and worry about commiting to enough lag to eat a usmash).
I think this is a better example of a good 2v2 match [it also has an incredible comeback] - they are all staying reasonably close, each having their own team strats and combos to execute, while trying to cover each other to avoid letting their own MK get combo'd or let the other team's MK put in a lot of damage quickly. Yes the 1v1s occur, but they are usually by design for gimping or trying to make the most of a bad situation for one of the players on the opposing team:
https://www.youtube.com/watch?v=I04ULNFyC2A
Incidentally, that doubles match is also the only time since like Apex 2012 that the losing team of that match didn't win the doubles event they entered.