Thanks for the helpful feedback. During my initial testing with the self-signed certificates, I installed those to the Machine certificate store. Since AnyConnect worked in that configuration, I proceeded to install the CA signed certificates to the Computer store as well. In hindsight, I suspect that I was signed into the machine as an admin which made those self-signed certificates in the Computer store accessible to AnyConnect.
What you suggested (installing the CA certs to User certificate store) worked so thank you for pointing me in the right direction.
With the new understanding that the User certificate store is where the CA certificates need to be, is there a best practice approach to prevent a non-privileged user from exporting the User certificates for install on a non-approved device?
In the end, we're aiming to limit AnyConnect VPN to just corporate assets. With AnyConnect/ASA, I recall that Dynamic Access Policies could further "inspect" the endpoint but that feature doesn't exist in Meraki's AnyConnect implementation.