Recovery of iCloud /email/ password

I am the rightful owner. I'm literally writing with my Apple ID email here. For some reason, I had two different passwords on my iCloud email/Apple ID. I think it's because iCloud email made me change it at some point, but it was in like May 2015, so forgive me if the details are a bit blurred. I always use a variation of the same password everywhere (it's a randomly generated password and I change a random character of it), and I'm good at remembering them, but I only had to type down my iCloud email's once since May 2015 because I was already logged in and it didn't ask me to enter it every time I wanted to use it. The problem is that I switched phones. I had an iPhone 6 and was gifted an iPhone 6s, so I have to re-enter the password to log in again and that's when the problem came. Since then, I've been trying to recover my iCloud for months, and it keeps saying that I have to wait a few days for it to be generated, despite the fact that I literally proved I own the Apple ID AND the phone. It didn't ask me for security questions and it didn't send an email to any rescue email. I would be able to do both of those things.

I'm from Argentina. There's no Apple ID Support for Argentina in that link, so...? Am I just supposed to say goodbye to that account? How incompetent can Apple BE? People forget their passwords all the time. There's literally no way to recover my email other than taking a 12-hour flight to ******* Mexico?

Read my first post, mate. I already checked that. There isn't one near me. The fact that you refuse to understand geography and that not everyone lives in a first-world country exasperates me. I don't have a reasonably close place to go. There isn't one. I'm not being dramatic. There isn't one. Do you have another solution?

I would never have to personally go to a place to get back my AOL, Gmail, Outlook or literally any other server's email. Only Apple would do something like this. Sadly, I didn't know that before creating that email and linking it to important bits of my life, or I would've stayed clear.

I have, yes. Sorry I've been so absent. What Fahmi_mac suggested worked. Of course, I could only access through my desktop iCloud. I can't add the address on Spark or any other app that manages several email addresses, but that's better than nothing!

Yes, but let me explain the issue again.

In early 2015 I got an iPhone 6. I created my Apple ID with a Gmail email. Let's say it was example123@gmail.com. The password was 123password. Right? Then it gave me the option of creating an iCloud email account, so I did. It was 123example@iCloud.com and the password was, idk password456, right?

Everything worked correctly. I had all my emails working on Spark correctly. In October 2016 I was gifted an iPhone 6S. I sold my iPhone 6 and started to set up the iPhone 6S (please note that I never changed my number). Logged in on my Apple ID with no issues. When I went to enter my iCloud password on Spark, it kept saying it wasn't correct. I tried all the combinations I could think of and it kept saying that it was wrong. So I went on My Apple ID to change the password. I thought it'd work like with any other password in any other email, right? You've forgotten it but you still have access to all the recovery settings, so they'll send a link to your recovery account or a code to your phone or a freaking pigeon messenger to your house idk. Something? Except... they don't.

This is what they say (I just tried it again. Please remember that I tried it the first time in last October, which was six months ago):

Apple ID Account Recovery

Account recovery is a secure and automatic process to help you regain access to your account as quickly as possible while protecting your Apple ID.

Depending on the information you provide, this will take a few days or longer.

'A few days or longer' is already too vague (and too long) to recover a freaking password when you have ALL the security settings up to date. But it's been SIX MONTHS. Nothing. Nada. I don't have an Apple Store close by to check in person. I can't call Apple Service because there isn't one for my country and they won't pay attention to me in the chat. So... I had no access until this lovely person above said I could check it on my iCloud on my laptop. But that's all I can do. I can't get notifications on my phone, so I have to check periodically to see if I've received any important emails, which is annoying and it makes me not want to use Apple any more, but at least I haven't lost access.

I had two-factor authentication on my iPhone 6 too and Spark worked anyway. I don't understand what you mean at all. I'm sorry, but it sounds like gibberish to me tbh.

I can't check my account recovery. When I go to iForgot the only way I can 'advance' a screen is submitting all the information again and it treats is as if I hadn't submitted it before.