Set MyFamily but hide it from public RelaySearch?

Hello,
I have a question regarding MyFamily.

The background:
I run two relays (and a bridge) on my servers. The systems are hosted by different providers, and I am regularly known to them by name.

I have been thinking about running an exit node for some time now. However, I would not like to run one on my own systems, as I don’t really want to be associated with the exit by name due to the potential consequences.

I have now found a provider who doesn’t take such a dim view of the fact that I have misspelt my personal details in several places. But now I have the following problem (probably caused by paranoia):
The exit node must be part of the MyFamily, if I add it, it is of course not difficult to find my other nodes from the exit. I’m not afraid of a request for information about my personal data to the ISP of my exit node, but a request to the other ISPs of the remaining nodes would make me a little nervous.

To the question:
Is it possible to include all nodes in MyFamily but not show the connection to the exit node publicly? My main concern is that this connection cannot be seen via the relay search, but Tor clients can see it.

No, is not possible, because this information is (as you already know) needed by every client, when building a circuit (so it has to be public). I have no proper solution in mind to solve your problem without rebuilding your complete tor-server-fleet from scratch, having this challenge in mind.

Another example, where the credo “Remember that running a relay is an act of transparency” does not really fit the need of all operators… There are proper reasons some people want to stay private, even if they decide to be an operator.