DEAR PEOPLE FROM THE FUTURE: Here's what we've figured out so far...
OP is correct that YourController::$paginate is only fed into the PaginatorComponent once. If you need to call YourController::paginate() again with different options, you'll need to unload the component first, e.g.:
$this->Components->unload('Paginator');
Then, the next time you call YourController::paginate(), it will reload whatever's in the YourController::$paginate property.