The weighting/scoring is applied by the database. In this specific scenario it is at the end because the filter adds its results to the “core” search results. It is not possible to apply a custom order on results in as far as the weighted score from the db is concerned.
Now, that said…
What you could do is alter the snippet I gave and perform a custom query taking the entry ID’s from the $scored array to sort them however you want. So you could order by type and alphabetically within that order. I do not have any custom code laying around like the snippet I gave you to accomplish this, so, it would custom coded.