What about setting up two mobile phone numbers for recipients of the recovery code: 123 sent to phone #1 and 456 sent to phone #2? (Phone #1 is yours and phone #2 is your elected trusted partner’s)
Doesn't have to be SO. It can be a trusted friend who knows in advance that you may voice call them in a password recovery scenario (voice calls not via text).
Edit: regarding the "lack of availability" at the point of wanting to reset the password: the urgency of resetting passwords should be considered a lesser inconvenience than the risk of having lost control of your account through insecure 2FA.
(I am simply supporting my original brain storming thought through ... I am not married to this idea in any way or form. Just a thought.)
Won’t this work?