Mattie snaps and tries to bite the cat's head off, so it seems
If mattie intent to injure the cat then that is eactly what she she would have done. The intent is move the cat away An it is porpably effective at doing so which is why she continues to do so, and is therefore in a more prime spot to get food.
as for solution consider the following.
I have never met a dog basset included that persist in "begging" behavior if the begging is not reward at least on a occasional basis. Stop rewarding the begging behavior and the begging stops and the need to protect the most valuable resource people food. I would be remiss however if I did not point out a phenonenom that occurs when you try creat a behavior extincting by not rewarding a previous rewarded behavior, That is know as an extinction burst. That is the behavior gets worse much worse and more persistent and aggresiviely applied before it goes away.
Another alternative to to teach an incompatable behavior. That is simply have her sit or lie and wait for you to finsh eating at a greater distance for the table and the cat at some other location doing the same thing. See
Table Manners For the cat you are likely going to need a better reward than stinkified cherrios however.
Change the prospects of being rewarded to the vaciniety of the cat. That is do not reward the beging behavior unless the cat is near by. And consistently reward the behavior when the cat is close. What this does is fundamently change the association the dog as made in regard to the cat and people food. Currently the dog associates the cat as a threat to its supply of people food. By reward the dog only when the cat is nearby we change the associate so no the pressence of the cat signifies people food gates will be open and the dog will become more tollerant Dare I say encouraged to have the presence of the cat while begging
There is never a perect solution just some bettter than other given the particulars of the situation it is why I provided variety of solutions than you chose from keeping in mind the obvious consequences of each.
Daisy will take the long way from one room to the other just to avoid Charles!
Which is precisely why the cat continues in the behavior. Because it is generally effective. If it did not affect the dogs behavior the cat would stop this behavior. That is not say it would not try something else to obtain the same results.
It sounds as though your dog is trying to establish his order in the pack.
you really don't want me to go their do you with the thousand of links and reason why the most learned and trained behaviorist find the whole pack heirarchy a myth when applied to dogs and dog training. Dog do not seek status. If fact if you had so called experts in pack heirarchy observe the same group of dogs they would reach different conculsion in which dog was alpha and the rest of the so called pecking order. The fact this can not be reliably done should be suficient reason enough not to buy into the notion, The dog is not seek higher status over the cat, no it is simply seek to gain more people food for it self. It is us humans that build the artificial and erronious constructs of status because they are important to us, not so for the dog what is important to him is the resource. Never mind the fact there is no evidence for interspecies packs as well.