This seems to work well:
=FRFISCAL("End",FR("Year")-10)

This didn't work for me either.  It just gives me current fiscal year end.  I have formatted the previous cells as dates.

It's strange to me that this formula [=@IF(@FRAMT("BALP.L11","4000:4999")<>0,FRAMT("BALP.L11","4000:4999")] works all the way to L21 which is my first year of data, but I can't get the Fiscal Year End to work.  It just reads the 1 not the 10, etc.

This didn't work for me either.  It just gives me current fiscal year end.  I have formatted the previous cells as dates.

It's strange to me that this formula [=@IF(@FRAMT("BALP.L11","4000:4999")<>0,FRAMT("BALP.L11","4000:4999")] works all the way to L21 which is my first year of data, but I can't get the Fiscal Year End to work.  It just reads the 1 not the 10, etc.

You should be able to test the formula by trying variations of"
=FRFISCAL("End","2010")  or

=FRFISCAL("End","2015")

Also, ensure you're clicking the F9 or FR View to set the current year / period