I dont think any change in GMail setting is not needed for integration with PRPC just giving the detail of SMTP or IMPA/POP of your choice would be sufficient. Just toggle the 'Use SSL' if face any issue.
If want to connect SMTP over SSL then try Port - 465 instead of 587 . I too faced an issue with SMTP with the detail you posted here. IMAP detail i tried from your post it is working fine. Let me know if this works for your or not ?
Please find attached configuration that i tried and it is working fine for me.
SMTP port 587 is commonly used with STARTLS connection security, not "SSL." The "use SSL" checkbox should not be checked when using port 587. Traditional STMPS (SMTP over SSL) can be done via port 465, but this is a legacy feature of gmail and port 587 is the preferred port.