Beautiful cat, bald nose not withstanding! The nose looks to me like a fairly classic case of eosinophilic dermatitis. That is an autoimmune skin disease of cats that can manifest anywhere on the body, but we most commonly see them on the lips (they are called "rodent ulcers" when found on lips), the nose, or the bridge of the nose.
I have seen all manner of severity, from bald patches and some thickening of the skin at the bridge of the nose like we see with your kitty, to full out ulceration and scabbing of the nose.
Eosinophilic are a line of white blood cells in the body that are involved with inflammation related to allergic stimulation. Hay fever, allergic skin disease, asthma, etc., is all mediated by eosinophil infiltrates. In the case of feline eosinophilic dermatitis, the eosinophils particularly hyper-respond to particular areas of the body, the bridge of the nose being one of them. Essentially, the kitty's own immune system is targeting the pigment and hair follicle cells in that region and causing loss of pigment and hair. Luckily in your kitty's case, it has not yet progressed to outright ulceration, but it could over time.
I do not believe that the tears are a cause for the issue, but a result of it. The nasolacrimal ducts open at the corners of the eye, and the junctions of the ducts and the skin are likely secondarily inflamed, leading to the excess tears.
Here is my advice to you, coming from a veterinarian who has a lot of experience treating this disease:
1.) Continue the limited ingredient diet, as these kitties tend to have multiple allergic pathways, some of which could be food induced.
2.) Ask your veterinarian to prescribe tacrolimus ointment, 0.1 %, applied two times daily. This ointment is an excellent remedy for autoimmune skin disease in dogs and cats, and I have had a g reat deal of success in treating this condition with it.
3.) Consider a round of systemic antibiotics concurrently, as secondary infection is often a complicating problem. There is an antibiotic called Convenia that I love for cats with skin problems, as it has great activity against common skin bacterial infection, and requires only one single injection.
4.) Use year round veterinary grade flea prevention, even if the kitty is indoors strictly. Even one single flea bite in cats prone to this disease can set off an outbreak, and the flea that we most commonly associate with dogs and cats actually is the "cat flea," which has the greatest affinity for, you guessed it, CATS. The cat flea will readily feed on a dog, but given the choice, it will go to a cat, as that is the definitive host.
Thank you for including a picture...it was most helpful in this consultation. Please feel free to print out my suggested diagnosis and recommendations to show your veterinarian for discussion.