I agree with talking to Johanna, but I'm still not sure about sinking 2/2 or 2/3 convos into it. I can see the argument that if we're going to do this, do it right though.
@Teen Spirit's comment alleviates my concerns about waiting too long on the progress, so I'm more in favor of leaving it until after our sibling's birth.
I'd prefer to do back-to-back training under the assumption that there may be some sort of tourney for our sibling's birth (or shortly thereafter, after they're confirmed living and healthy), and if so it's likely to be a relatively large tourney (which Tarly has said we need). Showing up and crushing it would be a show of strength - while it wouldn't be officially called that I imagine there would be those calling it the "Heir's Tourney."
Edit: On the other hand, if Viserys has soured on tourneys celebrating the birth of his children after the last time, maybe this won't happen.
I'd also like to get in a study: martial or study: diplo or train: ride. While
@Teen Spirit has said every action has advantages, so I'm sure there is one, I'm not sure why we'd be sneaking out into the city? In show canon, I think this pretty much only disadvantaged Rhaenyra. While a lot of the reasons for that are not present here, I don't really see any benefits we know about and it could still start unpleasant rumors. Also, IC-wise, show!Rhaenyra does this to get some freedom and escape her responsibilities, while quest!Rhaenyra is already taking her freedom and doesn't want to escape her responsibilities.