2a. No 2fa, so this is a reduction in my current security
That’s open to interpretation. Your current solution you thought was secure, but you used a service that as it turned out had bad security practices, which you just didn’t know (arguably couldn’t know). ANY online/cloud service that you don’t host yourself has this issue with being a black box of unkown quality. Any online service you do host has to be secured by you (or you need to trust that the base setup of that tool is “sufficiently secure”), and is in essence limited by your knowledge of the tool and technology used. Also if you’re reusing any passwords, anywhere, just stopping that practice is likely more secure in practice compared to 2fa in isolation.
2fa in general isn’t just plaing “better” than not having it, security is rarely this black and white. It also depends on what is allowed to be the “second factor”, and since yours included SMS, it really wasn’t secure at all (like others have also mentioned in this thread). And it depends on the password of course. For example if you use a really secure password (30+ characters), and don’t reuse it, it will in practice be more secure than a short(ish) password and a 2nd factor that allows SMS. Generally 2 factor is used as a term for 2 categorically different athentication methods: one thing you know (password, pin) and one thing you own (phone, physical device/key, or a file works too). The problem is that SMS doesn’t require your phone. It’s incredibly easy to get the SMS without having your phone (even easier with physical proximity) or flat out faking owning your phone number (dpends on a lot of factors how easy or hard that is in practice, doesn’t require physical proximity). Basically, if someone actively targets you and/or that account secured by SMS 2fa, it isn’t overly hard, but it’s good enough at preventing giving access through a data leak for example.
So, back to the security of “solution 2a”: how would someone get access to a long password you don’t use anywhere else, that isn’t written down anywhere (or nowhere accessible), and where you essentially never need to use/access the account in the first place? Nobody would even know that whole account exists unless you specifically tell them, let alone knowing how to get in. Note that this can also be combined with the concept in solution 4, so you’re then using it to only restore a single 2fa code. So that “safety net fallback account” very rarely needs to be updated with a newer Aegis-Backup, making it even more obscure/unknown. That 2fa code then lets you access your normal account and backups, and you restore the full suite of 2fa you need.
It boils down to this: local 2fa with a backup means you need to get access to a single file to securely restore full access to everything. That file can be transmitted insecurely (due to strong cryptography and hopefully a good password not used anywhere else), but I wouldn’t store it out in the open either. On the other hand, any cloud based solution is an inherent black box. You trust them to properly do things, and you only know they didn’t once it’s too late (like Authy). It also means they are, by nature of what they do (storing account access information), a target and if the attacker is successful, you’re the collateral without having been explicitly targeted. Maybe there are sevices out there that let third parties audit their security and publish the results, but I don’t know of any and it would probably increase the price by an prohibitive amount for most people.