@mitrione
WP Mail Bank will be no help to you at GoDaddy because GoDaddy blocks external access to ports 25, 465 and 587. Using the Gmail API through Postman SMTP is pretty much guaranteed to work at GoDaddy since Postman supports HTTPS as well as the standard SMTP ports.
Also, since you use Google Apps you may be required to use OAuth 2.0 which Postman supports but WP Mail Bank does not.
I changed one of the MX records to set up the gmail account which seems to be working properly
You might have done that correctly. You can copy my domain's settings if you want, hendriks.ca, it's also a Google Apps domain. MX, SPF and DKIM are all correct.
hendriks.ca. 3599 IN MX 1 ASPMX.L.GOOGLE.COM.
hendriks.ca. 3599 IN MX 5 ALT1.ASPMX.L.GOOGLE.COM.
hendriks.ca. 3599 IN MX 5 ALT2.ASPMX.L.GOOGLE.COM.
hendriks.ca. 3599 IN MX 10 ALT3.ASPMX.L.GOOGLE.COM.
hendriks.ca. 3599 IN MX 10 ALT4.ASPMX.L.GOOGLE.COM.
hendriks.ca. 3599 IN TXT "v=spf1 include:_spf.google.com -all"