Alright, so I was able to figure out what the heck I was doing wrong here. It comes down to me not having sourced the smime.rc file such that Mutt knew what OpenSSL commands to use when trying to sign/verify and encrypt/decrypt messages.
As an aside, just in case this is useful to anyone, I also figured out how to ensure I can read encrypted emails that I've sent to others when I look at them in my sent folder.
In smime.rc, update the smime_encrypt_command to tack your public encryption certificate onto the end of the openssl command. For example:
set smime_encrypt_command="openssl smime -encrypt -%a -outform DER -in %f %c ~/.smime/certificates/123456789.0" Where certificate 123456789.0 is your public certificate for S/MIME encryption. Just for completion, %a is the variable for which method of encryption to use, %f is the variable for the email text being encrypted, and %c is the variable for the recipient(s) of the email.