I'm active in the forums when I feel like my game is a bit rusty and/or I need a challenge. Here are some dos and don'ts that hopefully help you based on what I've seen you all (and myself) do.
But before that, standard disclaimer: I'm a moron who knows nothing. Take everything I say ever with scoops of salt and feel free to disagree. I'm posting this more as a reminder for myself before I forget. The opinions are purely my own and often there is no one right answer. This is just what one man (me) would do.

What to do and not to do when a girl's texting style is triple/quad texting

You are not required to reply to every single thread in the girl's messages and make a quad text reply yourself. You have the luxury of picking the interesting threads and only replying to those.

Example from a thread from earlier today

Her-Ahh the privelege
Interesting, my ex was half Greek cypriot, is that similar or not really
Spanish is cool
I like sports and food and I have a lot of pets...that pretty much sums me up wbu?

Me-Cypriot greek and mainland greek are the same, Macedonian not so much
Sí, especialmente a impresionar una linda chica como tu
Love to stay active through martial arts and climbing. Love cooking new cuisines and cute wine dates

His reply is to each and every thing she mentions. Speaking spanish in reply to "Spanish is cool" is DLV not DHV. I'd have ignored that. The first line could have been much simpler, because it's just boring. I'd have said either "no they're not similar" or "I'm contractually obligated to say I'm nothing like your ex" if you want to be less boring. Even completely ignoring that question would have been fine in my opinion. The last line is pretty much the only mandatory one here.

You do not have to mirror the girl. Especially her girly behavior.

"She triple texts all the time, so I figured it'd be ok if I did it too". Are you also a girl then? No? Then don't do it.
"She hearted/liked my tinder messages, so I felt like reciprocating". No, you don't have to. This might just be a pet peeve of mine, but there are plenty of ways to provide validation when the girl says something funny or worthy of applause. Almost all of them are through text (lol, cool, haha etc).

Girls can do weird shit and get away with it. You can't. It's your job to have your own identity in how you text and hold to it. If you're swayed by her texting this easily, then she's got no reason to respect you.

Do not insta text back and forth unless it's purely logistics

Texting has the fewest amount of pitfalls when it comes to game because you can take your time to craft a good reply. Why would you surrender this massive advantage by insta texting the girl live? I mean, I know why. You're way too eager. But the question is rhetorical. Don't do it.

I have a rule that I'm going to wait at least 5, if not 10 mins before I reply to a text. I come up with a better text than what I would have sent had I been insta texting at least 70% of the time in the 5 mins I give myself. One cringe text is all it takes to dry up that pussy. You can leave her message on read for a lot longer than 10 mins if you need time too btw.

One trick to organically achieve this is by turning off notifications from your apps. That is free impulse control. You're welcome.

Fastest way to improve game in my opinion

If you can think of a situation where you'd be stuck, it's probably somewhere here already. Solving (or attempting to solve) other people's stuck convos is a great way to get free experience. It's like texting a girl, without the downsides.

Another thing to do would be to look at the posts from all of Alex's comments and understand his thought process, then mimic that in your own interactions.

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I'm sure I'll think of more in due time and I may/may not update this post. But I hope this helps.