Hello Ray, I'm Dr. Deb. I'll do my best to help you today.
First let me express my condolences on the cat you lost in January; this must have been very difficult for you and your family, not to mention Branston.
And, I hope that you have also recovered from your health issues.
I have several thoughts about this problem with Branston.
There are several possible reasons why a cat will overgroom but if these two episodes are the only skin problems he's ever had, then there are likely to be only a few reasonable causes:
1. It sounds like his problem may be Psychogenic in nature which is what I suspect you presume may be the cause. This condition is exactly what it sounds like: cats overgroom their bodies because of stress or change in their environments. As you probably know, cats are very empathic and react to our stress as well as things which might directly affect them. Clearly, he has had quite a bit of stress and change to deal with!
It probably serves as a way of soothing themselves and helping to handle the stress/changes. However, having said that, some studies have shown that many cats previously thought to suffer from this condition actually have pollen allergies.
One way to differentiate this condition from other skin problems is that when these cats overgroom themselves, they tend to leave "peach-fuzz" type fur on their bodies; they are not actually bald or have sores like would be seen in for other allergies.
Treating this particular condition can be frustrating even when the triggering event (the other cat in this case) is known.
You might try a Feliway diffuser or spray; these are natural pheromones which can help instill a sense of calm and reduce anxiety.
There is also an oral product called Composure Chews which is formulated to do the same thing...to calm the cat.
I've had some owners who have had great success with these types of products and others who feel they are not terribly effective....so you won't know until you try them whether or not they will work. But I would definitely consider them; they are available on the internet and some pet stores might carry them.
2. Inhalant or pollen allergies can be responsible for overgroooming; they are reacting to such allergens as dust mites, mold, grasses, trees, etc. These cats can lick just about anywhere on their bodies with this problem.They may or may not respond to antihistamines (see below) but they almost always respond to steroids which can help with the diagnosis.
However, this particular condition would be very uncommon in a cat this age with no previous significant skin issues unless you've moved or installed new carpeting or new landscaping etc....something different to which Branston is now being exposed.
Antihistamines can help in some cases.
Diphenhydramine at a dose of 1/2 of a 25 mg tablet given twice daily or
Chlorpheniramine at a dose of 2-4 mg or
Loratadine (Claritin) at a dose of 2.5-5 mg or
Cetirizine (Zyrtec) 5 mg once or twice a day
It is important to ensure that the formulations used contain ONLY the antihistamine and are not combination products (e.g. Claritin-D contains pseudoephedrine, which could cause very significant adverse effects in a cat).
Sedation can be a common side effect with these drugs.
3. Fleas if he goes outside; less likely if he's an indoor only cat. You may or may not see fleas since they can hop off and on a cat's body and they can be ingested from all the grooming.Cats can become allergic to the flea saliva and literally one or two fleas can drive them crazy. The areas of their bodies that they tend to lick a lot are the spine in front of the tail and the stomach; sometimes the backs of the legs, too.
Your description of the pattern and timing of the overgrooming aren't terribly consistent with this problem but I include it to be complete.
4. There are other causes for overgrooming such as allergies to food or other parasites such as Cheyletiella but these really don't sound like possibilities in this case.
If I had to speculate, it sounds like Branston is suffering from #1. It's quite possible that his behavior will diminish the more comfortable he feels around the new cat.
I suspect you're already spending play time and "me" time with him, but perhaps give him more individualized attention which may also help reduce his anxiety.
I hope this helps. Deb