I can get product attributes efficiently without loading the entire product by using:

Mage::getResourceModel('catalog/product')->getAttributeRawValue($productId, 'attribute_code', $storeId);

However, I can only do this with the pric' attribute, since final_price is technically not an attribute. Since I'm grabbing a few hundred products on one page load, and the only data I need is the product's final price, doing this is very inefficient:

foreach($productIds as $productId) {
    $finalPrice = Mage::getModel('catalog/product')->load($productId)->getFinalPrice();
    ....
}

Since I'm loading the entire product. If anybody can suggest a more efficient way, I would really appreciate it. Cheers!