Dynamic range from every nth value in a column in a data validation list

I'm trying to create an array formula that makes a dynamic range from every nth value in a column and use that formula to create a data validation list in a cell. I've managed to conjure a formula that creates a dynamic array from every nth value in a column, but I can't seem to use it in data validation. Excel doesn't seem to like array formulas as a data validation source and using the formula to create a named range also gives an error. I tried to make an array range in a sheet and use that to create a data validation list, but I can't get rid of the #N/A-s even with IFERROR. Also my current formula doesn't work with strings. I'd appreciate if someone would help me make it work with data validation and with strings.
The formula is:

=IFERROR(SMALL(IF((Sheet1!$A:$A<>0)*(INT((ROW(Sheet1!$A:$A)+1)/2)=(ROW(Sheet1!$A:$A)+1)/2);Sheet1!$A:$A);ROW(Sheet1!$A$1:INDEX(Sheet1!$A:$A;COUNTA(Sheet1!$A:$A))));"")

See the attached workbook on how it works as an array range