If it were me, I would create a field on the Opportunity Entity named "OpportunityReminderSent ".
Then I would edit the filter on the workflow to include AND OpportunityReminderSent Does Not Contain Data
Then when the workflow runs, it uses the original criteria and the new "OpportunityReminderSent " field to determine Opportunities that do not yet have the "OpportunityReminderSent" populated.
Your workflow will then send the initial 13 month email reminder and the final step is to update the Opportunity to set the "OpportunityReminderSent" to the date the workflow sent the email.
Yes the modified on date will now change, but that no longer matters since you are ALSO looking for a blank/null "OpportunityReminderSent" and that won't be blank/null since you are sending the 13 month email for it.
The fact the modified on date gets updated when a value is written to "OpportunityReminderSent" is no longer a problem.
That will ensure the Opportunity is only actioned on with a 13 month reminder email one time.