I am hearing you about psychotherapy. Sometimes it can be like "Donkey for a Day" http://pooh.wikia.com/wiki/Donkeyfora_Day Which I think MLP:FiM ripped off.

As long as the DoA can determine what the baseline for that character is, they should be fine.

Actually, I am seeing a problem. They need to be more in-tune with the characters they are de-angsting. I imagine the agents in the hallways aren't the only ones who react negatively to glitter. For the Good Omens fic, I would have liked to see them try classical music and fluffing an old book in their face. (Shop should already have been saturated with the scent.)

It's probably the difference between fixing an extrovert, (you get them into their element by dragging them to a party,) and fixing an introvert, (wrap them in blankets and distract them with a good movie.) You don't fix an introvert by trying to turn them into an extrovert.

I'm going to look at the actual corpus for a minute, rather than just the Wiki (because older Wiki articles tend to be full of unsupported statements). There are only apparently two DOA missions (technically, by the way, Action departments have all-caps acronyms, so it's DOA rather than DoA):

-In the second mission, the only treatment seems to be stomach-pumping a badfic-induced alcoholic and then neuralysing him.

-In the first mission, we have this introduction:

Lasa clawed caked glitter out of her face and continued to rifle through the cupboard. ‘So did I. But that’s not what’s in the cupboard. Instead we have glitter. And balloons. Chocolate. Origami paper.’
‘Well the Aloe Vera told us we had to cheer up canon characters who were angsty. So I guess we-‘
‘What? Put on a circus act? Apparently that’s not going to be enough. Listen to this. We’ve also got an industrial sized jar of Prozac. An industrial sized jar of something called ‘PPC-modified Benzodiazepine - Addictive Properties Completely Removed!’ and something else called ‘Perphenazine; Completely Elf-Safe!’ And a book, mysteriously entitled ‘Psychotherapeutic Drugs for Dummies – A Reference for the Rest of Us.’’
‘We’re supposed to drug them? I thought the Department of Fictional Psychology handled that?’
‘Says here,’ and Lasa waved the synopsis of the Department’s ‘functions’, ‘that if they’re really bad then they do go to the DFP, but if we can deal with it ourselves, then we should. And, if possible, without recourse to drugs.’
Mombi hauled herself across the room and peered short-sightedly at the labels on the jars. ‘We’re going to have to come up with something else to call these. I mean, ‘Benzodiazepine’. It doesn’t exactly roll off the tongue.’ She pushed the huge jars of pills aside to reveal . . . more jars of pills.
‘What are these?’
‘Bleeprin,’ read out Lasa, ‘Can we give Bleeprin to canon characters?’
‘I guess,’ said Mombi uncertainly. ‘Ones that have been squicked really badly, perhaps. And look here;’ she hauled a bag out of the bottom of the cupboard. ‘We’ve got an exorcism kit.’

Then, in the actual mission, we have this:

‘Excuse me? The where?’
‘I think she means Hell. This angst is reaching excessive levels. Glitter rain time, I think,’ said Mombi, checking her wristwatch Angstometer. ‘Will you do the honours?’
Lasa took the glitter jar and the telescopic stepladder that Mombi fished from the Bag (which had been based by Makes-Things on Mary Poppins’ bag and had unfathomable depths. Mombi swore she had a particle accelerator in there, although Lasa doubted this) and, climbing to a height of about four feet, started gently raining glitter on the angsting angel. Mombi, constructing saccharine balloon-animals and origami figures, accidentally let one of her pink poodle balloons go. It bounced softly past Aziraphale, over each of his feet, and off into the opposite corner of the bookshop without him noticing. The atmosphere was starting to get so sweet and sugary that even Lasa started feeling slightly happier, but it appeared to have no effect on the angel. The blonde agent called down to her partner.
‘Mombi, this isn’t working. I think we’re going to need the light.’ Mombi rooted around in the Bag some more, and produced what looked like a torch. She passed it up to Lasa, who turned it on. Immediately the room was suffused in a warm, sunshine-like yellow light.
Still nothing.
‘What are we going to do? This isn’t working.’
Lasa thought hard, then switched off the torch and screwed the lid back on the glitter jar.
‘What are you doing?’
‘We drug him up, leave here, and go follow Crowley. The Words are recording some heinous errors there, and he’s coming to see Aziraphale. We nip back, grab a Bad Slasher and exorcise the pair of them. Two birds, one stone. Bang. Easy as pie. *Pigeon* pie.’
Mombi shivered. She quite liked pigeons. But she handed Lasa the spray hypodermic (blatantly stolen from the Red Dwarf continuum by Makes-Things, like so much of their equipment), packed with benzodiazepine, nevertheless.

And this:

‘Um, guys?’ began Mombi, tugging at Lasa’s sleeve. Lasa half-turned, impatiently, and saw what Mombi was worried about. Aziraphale was bouncing off the walls. Literally; his angelic powers being of great help here.

‘Ooooh, we’re screwed,’ said Trojie very seriously. ‘How much did you give him?’
‘The normal dosage for a human of his height and build,’ said Lasa, beginning to look concerned. ‘Why?’
‘Because supernatural beings have much more sensitive metabolisms than humans. Look, let’s sort out Crowley and then get to Aziraphale. Might have to take him to the Doc.’
‘We can’t leave him like this!’ cried Mombi. She was right to worry. The angel had spread his wings and was hovering around the lightbulb, making ‘pow!’ noises and incinerating things with miniature bolts of lightning. Intermittently he would hum snatches of the 1812 Overture.

This all suggests that the DOA has two methods: the circus act (which doesn't work), and the drug-and-neuralyse technique. Since - as Neshomeh pointed out - taking uncanonical drugs into Word Worlds shouldn't really be done, perhaps the next person to write the DOA should upgrade their techniques (based on the fact that their 'primary' method didn't work anyway): take a slower approach to the circus show that will lighten the mood over several scenes, and break them out gently. If that doesn't work - which it should most of the time - create a hybrid tasp-neuralyser which hits them with a concentrated burst of happy to break the angst-lock, then switches it off and immediately neuralyses them. If you wire them together like that, it would be impossible to misuse it (and leave them remembering the tasp effect, which could lead to addiction).

hS

PS: 'rede' means 'counsel', and is the word in the name of Æthelred Unræd. The OED seems to think that 'ready' derived from an unrelated (though identical) word; they link 'rede' to Middle Dutch 'raet, rait, raedt', but the root of 'ready' to Middle Dutch 'reet, reede, rēde, ree'. That latter suggests that 'ready' might be connected back to 'right' - as in 'upright'. I'unno. Linguij iz hart. ~hS