I think I'm in a similar situation and try to find out how to cope with it. The strategy I'm thinking about is - realizing what's happening (as you have articulated wonderfully), anchoring my self-worth else where (writing code / designing original solutions -> pushing what ever that's being discussed by those 3 people to an executable conclusion), finishing and delivering this project asap.
I guess the next step for me is to figure out how to avoid going into such situations (I entered the situation because I was joining a team in an area that I wasn't familiar with and decided to work on an existing project whose owner has a very strong presence and I didn't clarify the specific work item / boundaries clearly in the beginning).
Seems like you got a plan! How to avoid this situation in the future is also something I've talked about in therapy, and while I haven't reached a conclusion on that, a major takeaway from my session is that it's sometimes beneficial to not rationalize uncommon situations, as that can lead to self doubt and unnecessary guilt.
Even if we do get into a similar situation in the future, we'll be much better prepared to not only deal with it, but to identify it before it necessarily becomes a problem. To me that's the important bit.
I guess the next step for me is to figure out how to avoid going into such situations (I entered the situation because I was joining a team in an area that I wasn't familiar with and decided to work on an existing project whose owner has a very strong presence and I didn't clarify the specific work item / boundaries clearly in the beginning).