I’m not sure if David has further input due to his knowledge of his community, but I have seen websites in the past (admittedly few and far between) that utilize a javascript pop up box to lay out the process.
Here is your randomly created secure password, possibly add a “copy to clipboard” button, along with a short sentence stating; “use this password to login right now, if you wish to change the password, on the following page click ‘image of options button’ at the top of the page and select the password you want.”
It would eliminate the circumstance of forcing a user to leave the website just for going into their email, but would not really change the password security issue.
You could even adjust the automatic email to be sent out from immediately upon registration, to say 5 minutes AFTER registration auto-filling with the CURRENT login data. This gives the user enough time that if they want to change the password, they will receive an email with the password they chose for their records, or if the person decides to keep the original password, the email will reflect this.