I just tested my GoDaddy cPanel shared hosting instance (mail.griffin.software) several ways and got some odd results.
By including both intermediate certificates in the CA bundle...
TLS/SSL: Serves both intermediate certificates if I click to "update" the certificate, but serves only the R3 intermediate certificate if I install the certificate anew.
https://decoder.link/sslchecker/mail.griffin.software/443
SMTP: Serves only the R3 intermediate certificate.
https://decoder.link/sslchecker/mail.griffin.software/465
IMAP: Serves the default GoDaddy intermediate certificates.
https://decoder.link/sslchecker/mail.griffin.software/993
POP3: Serves the default GoDaddy intermediate certificates.
https://decoder.link/sslchecker/mail.griffin.software/995
I can definitively say that I recommend not using the long/default chain with GoDaddy cPanel shared hosting.
Your approach is probably the best here. Thanks for bringing my awareness to this absurdity. I will be cracking some skulls following up on this in the near future