Hi Jeff,
Sorry for getting back to you so late.
Rolling up 3000+ sites is a big process. Then the size of those 3-5 lists in your 3000+ sites is important. If the lists are big (thousands of items) then the rollup process will be costly.
I'd suggest to use QWP CAML filter feature to filter out all the information you don't want to display. If you could implement such architecture that you can split the sites/lists based on a logic that will help.
If you already started the implementation please let us know how that goes, any issue that you see, any tips that you could share with the community will be appreciated.