How did Mundungus convince the Order to use the Seven Potters plan?

Question

Prior to the events of the Deathly Hallows, Snape confunded Mundungus, on Dumbledore's order, so that the Order used the decoys as a plan to remove Harry from Privet Drive.

“You will have to give Voldemort the correct date of Harry’s departure from his aunt and uncle’s,” said Dumbledore. “Not to do so will raise suspicion, when Voldemort believes you so well informed. However, you must plant the idea of decoys; that, I think, ought to ensure Harry’s safety. Try Confunding Mundungus Fletcher. And Severus, if you are forced to take part in the chase, be sure to act your part convincingly. . . I am counting upon you to remain in Lord Voldemort’s good books as long as possible, or Hogwarts will be left to the mercy of the Carrows. . . ”
Now Snape was head to head with Mundungus in an unfamiliar tavern, Mundungus’s face looking curiously blank, Snape frowning in concentration. “You will suggest to the Order of the Phoenix,” Snape murmured, “that they use decoys. Polyjuice Potion. Identical Potters. It’s the only thing that might work. You will forget that I have suggested this. You will present it as your own idea. You understand?”
“I understand,” murmured Mundungus, his eyes unfocused. . .
(Deathly Hallows, Chapter 33, The prince's tale)

And, of course, Moody and the Order couldn't use their initial plan, as Moody himself explains:

Moody dropped his sacks at his feet and turned to Harry, “As Dedalus probably told you, we had to abandon Plan A. Pius Thicknesse has gone over, which gives us a big problem. He’s made it an imprisonable offense to connect this house to the Floo Network, place a Portkey here, or Apparate in or out. All done int he name of your protection to prevent You-Know-Who getting in at you. Absolutely pointless, seeing as your mother’s charm does that already. What he’s really done is to stop you from getting out of here safely.
“Second problem. You’re underage, which means you’ve still got the Trace on you.”
“I don’t—”
“The Trace, the Trace!” said Mad-Eye impatiently. “The charm that detects magical activity around under-seventeens, the way the Ministry finds out out about underage magic! If you, or anyone around you, casts a spell to get you out of here, Thicknesse is going to know about it, and so will the Death Eaters.
(Deathly Hallows, Chapter 4, The seven Potters)

But I'm sure the members of the Order could've imagined many other ways (and maybe even some that might have been safer) to get Harry out of there. Just for example (and I'm no Auror nor a member of the Order, so imagine what THEY could have thought to):

• using the Polyjuice Potion the other way, so that NO ONE looked like Harry (the answer to why they didn't do so is here, but that does not mean no one in the Order would have thought of it)

• letting Harry escape with speed and discretion, disillusioned and flying his Firebolt;

• like the Dursleys a few minutes earlier, driving a few miles, then disapparating or using a Portkey

• or other possibilities, some of them being discussed there.

So how did Mundungus convinced the other members of the Order to adopt his plan*?
(I was never under the impression that he was much loved nor considered any brilliant mind among the Order.)

*Other than telling them "We need to do so, otherwise there won't be any battle of the Seven Potters" of course!

Answer 1

Mundungus is an important part of the Order.

‘How come he’s in the Order?’ Harry said, very quietly.

‘He’s useful,’ Sirius muttered. ‘Knows all the crooks – well, he would, seeing as he’s one himself. It pays to have someone like Dung around, he hears things we don’t. -Order of the Phoenix

Mundungus, as a career criminal as the skills needed to hide, and has street smarts.

‘Mundungus, of course,’ said Sirius, and when they all looked puzzled he laughed. ‘He was the witch under the veil.’

‘That was Mundungus?’ Harry said, stunned. -Order of the Phoenix

Mundungus offering an idea on how best to hide Harry during an extraction, is just the kind of advice the order would actually take from him. Since his whole life is about hiding, avoiding notice, and misdirection.

Despite being a crook, Mundungus was also still trusted enough to guard Harry, despite being semi-unreliable. Even after his mess up over the summer they still used him to tail Harry when needed.

‘What do you think he was doing?’ said Sirius impatiently. ‘Keeping an eye on you, of course.’-Order of the Phoenix

Depsite our out of world knowledge that the plan may or may not actually be a good idea, the fact that in world Dumbledore originally came up with it, and states

said Dumbledore. However, you must plant the idea of decoys; that, I think, ought to ensure Harry’s safety.

Means that in world it has sound logic to it, and so with Mundungus's background, laying a logically sound plan out, it won't take much to convince the rest of the order.

Answer 2

It is implied that the Order did not have any other ideas that they thought could work. Thus, Mundungus convinced them by simply proposing an idea that they thought could work. From the conversation when the plan is explained to Harry (my emphasis):

"Let’s have no more arguments. Time’s wearing on. I want a few of your hairs, boy, now."

"But this is mad, there’s no need —"

"No need!" snarled Moody. "With You-Know-Who out there and half the Ministry on his side? Potter, if we’re lucky he’ll have swallowed the fake bait and he’ll be planning to ambush you on the thirtieth, but he’d be mad not to have a Death Eater or two keeping an eye out, it’s what I’d do. They might not be able to get at you or this house while your mother’s charm holds, but it’s about to break and they know the rough position of the place. Our only chance is to use decoys. Even You-Know-Who can’t split himself into seven."

Answer 3

I think you have already answered your own question in the question itself; however, I will leave an answer.

‘You will have to give Voldemort the correct date of Harry’s departure from his aunt and uncle’s,’ said Dumbledore. ‘Not to do so will raise suspicion, when Voldemort believes you so well-informed. However, you must plant the idea of decoys – that, I think, ought to ensure Harry’s safety. Try Confunding Mundungus Fletcher. And Severus, if you are forced to take part in the chase, be sure to act your part convincingly ... I am counting upon you to remain in Lord Voldemort’s good books as long as possible, or Hogwarts will be left to the mercy of the Carrows ...’

Now Snape was head to head with Mundungus in an unfamiliar tavern, Mundungus’s face looking curiously blank, Snape frowning in concentration.

‘You will suggest to the Order of the Phoenix,’ Snape murmured, ‘that they use decoys. Polyjuice Potion. Identical Potters. It is the only thing that might work. You will forget that I have suggested this. You will present it as your own idea. You understand?’

‘I understand,’ murmured Mundungus, his eyes unfocused ...

_{Deathly Hallows}

Snape used a Confundus charm to plant the idea in Mundungus of suggesting to the Order that they use Polyjuice potion/the seven Potters scheme to get Harry out of No. 4 Privet Drive. Mundungus presented this idea at an Order meeting, and it was selected by the Order as the best method to use to extricate Harry. _{-Deathly Hallows}