The issue appears to have been due to precisely what was expected. One of the domains was in /etc/localdomains and should not have been (the .com domain that was the recipient of the email).

Because that domain was hosted on the machine but using an Exchange server off the machine for email rather than local email, having that domain in /etc/localdomains meant the email tried to route locally and the domain couldn't process those emails.

By changing the domain to be in /etc/remotedomains via selecting "Remote Mail Exhanger" in WHM -> DNS Functions -> Edit DNS Zone for the domain, the domain was then able to be emailed from the other account.

If a domain is on your machine but email is not hosted locally on that same machine, that domain either needs to have the MX record modified on that machine or the domain needs to be changed to "Remote Mail Exchanger" upon editing the DNS zone in WHM.