Elementary PKINIT questions (MIT Kerberos/Linux configuration)

Dear kerberos community,

I've set up a very small MIT Kerberos installation for my own use, with 
MIT Kerberos under Linux. In experimenting with the PKINIT 
configuration, I have essentially followed the MIT Kerberos 
documentation (using openssl to generate keys and certificates), and 
reached the point at which I can authenticate as principal "jason" 
without a password. (I also have ssd configured on my Linux client with 
sssd-kcm for caching and the PAM module for login.)

First problem: I have a second principal, jason/admin, for use with 
kadmin. I've generated a certificate that can authenticate. However, now 
that I have two certificates (one for jason and another for 
jason/admin), it isn't clear how to configure the client to offer the 
correct certificate to the kdc. If I specify both certificates on 
pkinit_identities lines in the client's krb5.conf file, "jason" can log 
in, but kadmin returns a "Client name mismatch while initializing kadmin 
interface" error. My assumptions is that the wrong certificate was 
offered to the KDC (i.e., not the jason/admin certificate). Specifying 
the directory containing the certificates in pkinit_identities results 
in finding two certificates where one is expected, with an error message 
to that effect.

Do I need to specify a PKINIT certificate matching rule, or is there 
some other configuration that is required?

Second problem: securing the client's private key. The Linux client has 
a TPM 2.0 module, but I haven't found any documentation on how to 
configure it for use with Kerberos, if indeed this is supported. 
References would be welcome.

The machine has a smartcard reader, so my other options would be to 
purchase some compatible smartcards (after finding out what those are), 
or a security key. In the latter case, I would probably choose a FIDO 2 
key with smartcard support.

As mentioned, this is simply for my own use/experimentation, so there's 
no urgency at all.

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