Floating periodic calendar events without using recurring records

I think that you are very close.

Try this

var date MaintDateIfValid = FirstDayOfMonth(Today())+(Days([Assigned Day of Month]-1)); // subtract 1 so the 1st of the month is the first of the month

var text AssignedMonths = ToText([Assigned Months]); // convert multi select field to text to text

IF(
Contains($AssignedMonths, "All"), $MaintDateIfValid,

Contains($AssignedMonths, "Jan") and Month(Today())=1, $MaintDateIfValid,

Contains($AssignedMonths, "Feb") and Month(Today())=2, $MaintDateIfValid,


etc .....


Contains($AssignedMonths, "Dec") and Month(Today())=12, $MaintDateIfValid)