We have tested my idea in 6.35 and it works indeed. Again not a single programming code required (just file format code).
So let's say you have single project file and several WLs that you want to test with that project sequentially... Solution as mentioned... batch feature.
Now important action... first you need to export your WLs to file (e.g. tls file).
So in Symbols window right click each of your WL you want to include in same analysis project test and choose "Export" in context menu for each one of them:

Now in next appearing export window name them e.g. list0, list1, ..., list10, ... or whatever.
Next you need to create format file (e.g. name it TLSimport.format
) to be placed to Formats folder.
Note: in below format code you can see defined WL 63. That sample WL is used for all exported WLs (tls files). You can specify different one (WL number) but it has to be same one in all further actions.
Single format file needed only (so don't create multiple ones. it is needed just single one):
$FORMAT Ticker, Skip, Skip, Skip, Skip, Skip, Skip
$SKIPLINES 0
$SEPARATOR ,
$CONT 1
$GROUP 255
$WATCHLIST 63
$AUTOADD 1
$DEBUG 1
$NOQUOTES 1
Now create project file and in Apply to: Filter window choose same sample WL 63 (or your own one).
Then save project file after everything is set.

Next we create batch (and save it). Picture below shows batch of two WL changes. You may add more (as much as you want -> e.g. same as number of existing TLS files). You just need to add commands: "Clear watch list", "Data import ASCII" with path to TLS file and parameter of format file location, "Optimize" command and then "Export to file" with path and separate CSV file name for each result list export. So four batch commands per each WL. (Project needs to be loaded just once at start of batch).

When you choose "Data import ASCII" action to browse to WL symbols file then choose Files of type -> All files so that you can find your saved TLS files on HDD.

When batch is finished then save it and run it (via whatever method).
That's it.
If you have dynamically changing WLs then you could possibly use TLS files of DataBase's subfolder WatchLists. But you would have to add "Save DataBase" batch command before each "Data Import ASCII" command. Not tested though!