The reason I prefer a more delicate approach are two fold. For one, we don't know what plans Otto has for Alicent. This is a huge thing he'd be agreeing to. It may not be settled in a single conversation, and confronting Otto, having him say he'll think about it, would cast a sour note over the whole escape. Better just talk to Gwayne and ask him to handle it while we are gone, and finalize the arrangement by our return, by which point Otto would have actually gotten enough use out of our political favor to fully appreciate it's benefits.
As for Orwyle, the man is terrified, and what are we going to tell him? That we broke our oath and it's daemon he has worry about instead? Daemon who is far more unpredictable, cruel, and who may linger in Kings landing after we leave and potentially ask questions about Viserys's health after we leave? Handling this so abruptly and then running off for half a year leaves so many ways for this to go wrong and have us coming back to a mess. It's rushed and I'll thought out. trying to brute force a matter which requires finesse by hitting it fast enough.
I think given we now have a strong indication Viserys's mood effects his recovery, it would be wise to interact with him before we leave for half a year, especially given Johanna's pregnancy and it's endangered state. Johanna herself should certainly be spoken too as well.
I also think going out on the town while it's no doubt full of rumors and speculation about who murdered the maester's will only stress Rhaenyra out further. Just not a good time for it. Instead, let's get away, and focus on something less recently terrible, by flying to Harrenhal.
Lasts, some harp practice for stress release, but we don't need to much stress release, because we can dedicate the most of turn 18 to it.
[X] Plan a More Delicate Approach.
-[X] [Conversation] Speak with Viserys
--[X] Talk about anything else (About what you two have achieved and what the future will bring)
-[X] [Conversation] Speak with Gwayne Hightower
-[X] [Conversation] Speak With Queen Johanna Westerling
-[X] [Conversation] Speak with Isembard Arryn
-[X] [Action] Harp Practice
-[X] [Action] Fly to Harrenhal
-[X] [No Cost Action] Design Personal Heraldry
[X] Plan a More Delicate Approach Extra Hightower.
-[X] [Conversation] Speak with Viserys
--[X] Talk about anything else (About what you two have achieved and what the future will bring)
-[X] [Conversation] Speak with Gwayne Hightower
-[X] [Conversation] Speak With Queen Johanna Westerling
-[X] [Conversation] Speak with Martyn Hightower
-[X] [Action] Harp Practice
-[X] [Action] Fly to Harrenhal
-[X] [No Cost Action] Design Personal Heraldry
So, two plans, since speaking to either member of authority in the RTA seems wise.