Creating separate annually-repeating events is one solution, but you could also make use of a custom recurrence rule. Although Google Calendar doesn't allow you to directly create or modify arbitrary recurrence rules, the iCalendar specification which it uses and understands is quite robust in this regard.
Create an ICS file with a custom recurrence rule (RRULE). For example, to create an all-day event reminding you to reset your watch calendar to "1" on the first of March, May, July, October, and December each year, starting 1 March 2019:
SUMMARY:Set watch calendar to "1"
If, instead, you prefer to have an event at 22:00 on the previous day remind you to set it to "31" before bed, so that it rolls over to "1" at midnight, the following makes use of a negative
BYMONTHDAY value to pick the last day of the month (and therefore properly accounts for leap years, too!):
SUMMARY:Set watch calendar to "31" before bed
To import the ICS file (as of March 2019): Click the gear icon and select "Settings", then choose "Import & export" from the menu. (Here's a direct link as of March 2019.) Under "Import", select your ICS file and upload it to the desired calendar.
Of course, you won't be able to tweak the custom recurrence rule from within Google Calendar, unless you want to replace the recurrence rule entirely with one of the standard options. Otherwise, you'll have to delete the event, tweak your ICS file, and reimport. You should still be able to make other changes to the event within Google Calendar, such as renaming, moving to another calendar, etc.
If this helps, you may wish to read more about the flexibility offered by custom recurrence rules in the iCalendar specification.