OK so your Switch has a unique key embedded within it. It sends this key to Nintendo which checks it against a list and sees if it is on its list of valid keys.
Hacking Nintendo's servers to add your key back in or add a new one you made in is generally deemed beyond the pale for this one. Even if we were inclined to do that it would be a very hard task. For the effort we might as well recreate Nintendo's server setup and do that instead.
To this end you need to get a valid key and figure out how to get it to present this key back. We know something of how this key exchange goes down and it is not a trivial text file or something you can overwrite -- instead a lot of stuff happens in a hidden section of CPU designed for the purposes of security. Said hidden section is limited in what it can do and we do have some abilities to take a peek at what is happening there thanks to some vulnerabilities that were discovered. To that end it seems reasonable to be able to rewrite the relevant aspects of the firmware to speak to something else, emulate this hidden section's functionality in normal code and use a valid key to essentially unban yourself. At this point this emulation is not done, the things needing to be emulated are not known (leaving you to have to take a peek behind the curtain to figure it out), and the locations in the firmware where such things are checked are also not all known, oh and it will likely change for every firmware so you will have to either redo it every firmware update or figure out how to fake newer firmwares on older ones (and Nintendo can trivially change it radically as far as the hacker is concerned -- change a whole bunch of function names, add a bunch of useless functions, add a whole bunch of extra busywork steps to existing functions...).
You will then need a valid key. People can dump them (it is what people are using to access Nintendo's CDN) but the only place we know of is other Switches, and we are unlikely to stumble upon the generation algorithm for them (I doubt even Nintendo is that bad at it -- such things have not really happened for decades at this point and people know to use random numbers and list them, rather than generation methods). To that end buying another Switch, hacking another Switch and sharing a key (which better not be online at the same time) or similar are your options there. To do this at all "legitimately" is going to cost or need to find someone willing to give up theirs (possible but not much of a market for it yet like there was for the xbox 360 key vaults of 3ds friend code seed), less legitimate methods (don't know if we have exploits you could set up a fake pokemon event station for to grab unsuspecting peep's keys, and return fraud, offering a hacking service at school or something...) are all you though.
This is all things that have been done in the past, and seem well within reason (if slightly harder than some previous efforts) here. The desire to do it though does not seem there -- I think we are more likely to see XCI support on the open source firmwares before then. Your father is likely correct in this case but the effort required is considerable, and if the only perk at the end of it is the ability to now pay for Nintendo's online efforts... I am out.
Going a bit more black hat then if you did have key lists, a lot of proxies and the will to do it then you could ban swathes of keys, including valid ones. This would presumably cause Nintendo to cease banning for a while until they got a handle on things. Your existing banned key is unlikely to be restored to working status as part of this though.
