Can a conditional date be recurring? Such as every Feb. 1st (without the year)

Maybe you can use meta query to skip the year on the query.

So maybe it works if you use m/d without year.

For dynamic data after the : decides its input
{current_date:m/d/Y}

If you use ACF for custom fields you should be able to determine how to input it. Maybe set up an ACF data field instead of Bricks.