Boxward does not require the SMTP email to be the same as the IMAP email. If you are using a sender like Mailgun or Sendgrid, you can set up the email in Boxward using the SMTP details from that sender, and then use another inbox, like a personal Gmail, for IMAP.
Use the custom SMTP/IMAP setup option in Boxward
Make sure you have 2-Factor Authentication active here.
Then create an App Password here (Be sure to keep this App Password value as it will be used!), with App: Mail, Device: Other, and Custom Name: EmailWarmup
It will look like this:
Make sure that when you are connecting the email in Boxward, you are entering your 16-character app password, not your Google login password.
Here are all of the values for IMAP:
IMAP Username: [Your Gmail Email Address]
IMAP Password: [Your App Password]
IMAP Host: imap.gmail.com
IMAP Port: 993
Please ask your SMTP email server host for the SMTP settings that you should use.