If the top down method is the right way to identify a species, then brute force is the wrong way. Starting with a set of possibilities, you walk through them one by one, reading a detailed description of each, until you find the correct match.
It's easy to find a detailed description of a species on the internet. Just google the scientific name. What can be more challenging is to find a description of an order or family with easy to identify field marks that are common to all members of the family. Resist the urge to only look at pictures if there is a written description available. Some plants and animals are highly variable within the same species (humans for example), and some are so similar to other species that they can only be distinguished by dissection.
This method is only feasible when you have a limited list of possibilities and some confidence that your specimen is on the list. That's why it is especially important to be working with a good checklist. When using the brute force method, you should walk through your entire set of possibilities. Don't stop at the first possible match. That way you will know if there are other equally possible matches.
The best way to narrow down the list is with the top down method. Sometimes one gets stuck with that method (for example if the keys refer to a field mark like roots that you cannot examine). If that happens when there is a relatively small set of possibilities remaining, then the brute force method is an option. The definition of "small set" depends on your own patience.
If you find yourself trying to brute force your way through a long list, then perhaps you did not do your homework. Learn some of the field marks that are commonly used to distinguish the families (or orders or genera). Then when you start walking through a new family in your checklist, see if you can eliminate the entire family. At least this way you are using the top down method in some cases. Of course it is possible that your photos and notes simply do not show enough detail to make a good observation. In that case remember that it is better to make a high level identification ("it's a bird!") rather than a wrong one.