If you buy from reputable registrars, a domain name is propagated within 2 hours usually.
Meanwhile, if you do that people will know who that custom domain belongs to quite obviously.
SimpleLogin makes it look quite bad/complicated because of its UX yes.
In short and simple, I recommend:
- buy yourself some Addy.io account by either paying with monero or gift card via Proxystore
- get yourself a brand new (free) Proton account (no need to pay for anything)
- link both together, alias Addy goes into Proton
- never share/use the proton email and don’t use it as a mean for communication with friends/family, prefer Signal
No need for a domain name. Less portable but more privacy + less configuration to do.
No, alias for everything.
If for humans, share a public Signal username.
You could have a more private Signal username for your close family.
Otherwise (if trustworthy), you could also just share the Addy account with your family and let them manage the aliases themselves, kinda what I explain here. You could then have 1 alias into 1 or 2+ main email accounts.
Also, prefer to avoid people doing things for you as much as possible.
Download the data from each of the 3 accounts for backup purposes (in case you forgot to retrieve some info there).
Then delete all of them. Update the emails on places using it beforehand too if needed.
Why stressing yourself with a deadline here?
I’d focus on doing it right rather than doing it quick. 
You could have an anonymous Proton and anonymous aliasing.
Meanwhile, if you pay for either with your regular bank details, you’re not really anonymous for either no more. Hence my solution above without any KYC.
When you read something, consider asking yourself if you should be considering that or not.
Not everything common/achievable should be your way to do things.
I meanwhile would never share my Proton email account.
Why not for the alias system 
but not the main email box. 