In find mode, set field can enter search criteria into a calculation field so this is not a problem.
Make your pop up field a field with global storage and then this script will find your records by the specified fiscal year:
Enter Find Mode  ---> clear the pause check box
Set Field [YourTable::YourCalculationField ; "9/1/" & YourTable::YourGlobalYearField & "..." & "8/31/" & YourTable::YourGlobalYearField + 1 ]
Set Error capture [on] ---> keeps no records found dialog from interrupting the script if no records are found
Perform Find 
It's also possible to define a "fiscal year" field in the records being searched that calculates the fiscal year and then your search criteria is simply the contents of your pop up field.
Thanks PhilModJunk. That solution worked. I was very close in my initial attempts but had a few syntax issues in my calculation. Also, after I put in your code it wasn't working and I dug a little more and saw that I had originally created my global field as a date field, even though I was just inputting the 4-digit year into it. Once I switched that to a text field it worked fine, so I had a few issues.
Thanks for the help...again!