This answer isn't what you're going to want to hear, but it is correct since you've specifically said you aren't interested in cheating or boosting.
When speaking about competitive play, there's no easy way to win. And when speaking about competitive play that forces you to play against tougher opponents as you progress, it's even harder.
What you need in order to win competitively is the same thing everyone else needs: experience.
When players get a good rating (especially in their first season played), it's because they put in the hours. They learned the ins and outs, built the muscle memory, learned how their opponents typically act & react, and mastered their class. The most well-known players are the ones who use a very limited set of add-ons (if any at all) and generally don't use "fancy peripherals" (though some of them do).
But the one thing they all have in common is experience. There's no substitute for it. It applies both to PvE and PvP. Things are easier when you have ample experience with them.
If you have the time to dedicate, many experienced players can attest to 2k rating not being that hard. But when it's your first time going for it with a partner who you've never done it with, it will be time-consuming. You need to be dedicated. Treat it like raiders treat raiding:
- Have a set schedule of 3+ straight hours and play through that entire schedule 3+ times a week.
- Pay attention to what works and what does not. Check the combat log for what killed you and ask yourself why.
- Ask questions and take advice from experienced players.
- Understand your opponents' abilities as well as you understand your own.
And specifically for PvP, record yourself playing and then re-watch it. See if, from a spectator's point-of-view, you would have done this or that differently. And then think of why you didn't think of doing that in the moment.
Now that THAT'S out of the way, here are things that you can do to ease the steepness of this uphill climb:
- Get geared, fast. Gear is the cornerstone of this game. The best gear is from Conquest Points, which have a weekly cap. You want to increase that cap as high as you can as fast as you can, typically aiming to get the highest RBG rating you can possibly get in your first week with a lot of dedicated runs. The longer you wait, the more irretrievable points you'll never get. As for your initial set of gear with Honor, there are honor farms running all the time. Using tools such as oQueue can help you find these groups fairly easily.
- Incrementally set up add-ons. Though some PvPers swear against add-ons, add-ons can immensely improve your awareness, which is essential for new & learning players. Learn which buffs and debuffs are important to look out for but may not be entirely obvious (Devouring Plague, Unstable Affliction, Master's Call, etc.) and make them visible on your UI. Remove things as you care about them less or understand them more, and add new things as you feel they apply. It doesn't matter how you see them. It only matters that you see them. The rest is up to you.
- Bind your keyboard, hardcore. WoW is on the short list of recent MMOs that can take up your entire keyboard with. If you ever find yourself queuing up the wrong spell or being unable to move and cast at the same time, then you didn't bind your keys well enough. Making use of your mouse (eg. mouse wheel up and down as spells instead of zooming), setting your movement keys to ESDF instead of WASD to free up more easily accessible keys, etc. Anything you can do to get more skills in easier-to-reach places will improve your reaction time and accuracy.
- Macro everything. Macros are a privilege. Use them often and use them wisely. From quickly targeting with
/tar arena1 to using all of your non-GCD burst spells at the exact same time, macros will improve your efficiency.
- Duel people, especially people who can beat you. Ask them what you are doing wrong. Be friendly and never engage in an epeen battle. If they are attempting to antagonize you, don't feed the troll. Just duel someone else. You get the best tips about your mistakes from people who profit from your mistakes. They know exactly what you are doing wrong and are usually willing to tell you about it.
- Play a strong composition. Your class matters less than your overall composition. The composition matters more as you go to the smaller arena sizes (3v3 and 2v2). The raw potential of your composition can oftentimes overcome the skill of your opponent because some compositions just have incredible synergy. I no longer play so I can't give you a run through of the best compositions, but ask the PvPers "what's OP?" and you'll find out pretty quickly.
- Play with the same people. This goes hand-in-hand with the last point, but switching partners often is likely only going to set you back in your goal of achieving rating. Players tend to gain a good level of synergy with each other and switching not only means you have to rebuild synergy with a new person, but it also means that you need to rebuild synergy with the first person the next time that you play (though, it will be noticeably faster).
- Use voice communication and be vocal. Tell your partner what you are doing. Tell them what you need them to do. Tell them when you need assistance or when you make mistake. Be open and honest with them. Fess up to your shortcomings and assist them with theirs. It's your job to make each other better and if you aren't doing that, you'll be stuck at the same rating forever.
I'm not sure what kind of time-constraints you've put on yourself for this, but this will take time. If you are capable of putting in 8 hours at a time, daily, while objectively gauging your skills and correcting your mistakes, then I can see you achieving this goal in one season. And if you find partners that are experienced and willing to take you under their wing, you'll get it done in no time at all.