How about moving the mapping to module instead of a list? Create a module with week time scale, add a line item and format it with alt weeks list. Then use the drop down to map real weeks to alt weeks. Then your formula would look like: new module.alt week.
Agreed with the previous post, it is best practice to use modules rather than list properties
Also ensure that the line item to show the alternate week should only be dimensioned by time, not the lists as the alternate week won't change by list item. Doing that will save a lot of space and calculation time
If there is a logical way to conclude the correct member from alt weeks list, you could use finditem-function to automate the mapping. If there is no formula for that, I would probably build the mapping in excel, save that as csv or txt and would import it to module. If imported data includes the exact names or codes of your alt weeks list, Anaplan will populate the dropdown lists with the values. You can also use the weeks list as a source for the import action.
If you want to sum the alternative weeks to a higher level, build a parent hierarchy for alt weeks list or create additional list formatted line items to the mapping module that you can use with SUM: in your formulas.