Use an alternative mailer solution, other than PHPMailer in WordPress installations.
This package includes Swift Mailer for PHP 4 and PHP 5 versions. It enhances the option set over Shiftthis SMTP plugin and allows for Sendmail and PHP native mail() solutions with SMTP. So everything you can do with Shiftthis, you can do with this plugin plus more.
This plugin does not automatically handle attachments like Shiftthis SMTP plugin does, however this plugin works more like the built-in plugin that WordPress has. You should be able to access Gmail accounts just like Shiftthis plugin.
If you send email using the HTML content type, then this plugin will help you out and prevent the email from being picked up as spam by sending HTML content email with both HTML and plaintext headers. This allows email clients which don't support HTML to still read the email, while still benefitting those that do have email clients that accept HTML. You can not disable this feature.
The donation link is to the author of Swift Mailer, so please donate to the coder.