I suspect you're right about that.
I've taken lots of data with the Lasko fan and various filters. I have no data for the multiple filter arrangement but that won't stop me from speculating! So, making an assumption about the actual fan curve I get this:
More Filters 2.jpg
It looks like a case of diminishing returns for more than two filters with the difference between three and four not really worth worrying about. I would just skip the top filter and make it a solid top.
@OP, Did I read correctly, you're a RN with a wood stove in your house and don't have an AQ sensor?