I don't really know about cat urine, but some dog urine kills grass easily (typically females). Its caused by excessive nitrogen that burns the roots. I would have watered heavily at the time to try to dilute the affect right away. But by now the plant has absorbed it and will either recover or not. (yeah, real helpful I know). Definitely do not fertilze it (more nitrogen). I have read that garden gypsum is a good solution for the dog urine in grass problem. If cat urine has the same damaging properties, perhaps a little gypsum will help. Gypsum is also good for neutrilizing the affect of road salts on plants near the road affected by salt spray. And as nikkilyn stated, it may respond to cutting back. Most houseplants will. Plus if it is 20 years old and ceiling tall, it probably could stand some pruning and rejuvenation.

I agree with fred. If this plant were given to me, I'd whack it back to about a 6 inch stub and allow the new growth to emerge fresh and ready to grow. The plant is likely to grow multiple stems, creating a full and shrubby plant. At the very least, if given plenty of light, the new trunk will be a sturdier. I'd repot into a new, very porous potting medium while you're at it. Both of these chores can wait until early spring for a less stressful experience for the plant.

How deep is the mulch? And is water/rain getting through it to the roots? Perhaps dig up one plant to see what's going on underground. Oh yes, dahlias blacken if damaged by cold. Have you had colder than usual temps? As for the holes, finding out just what is chewing requires a bit of detective work. Look during the day, also at night, say about 10 pm or so. Be certain to investigate the undersides of the leaves as well as the tops.

Monstera is a zone 10 plant. New Orleans is probably 9b but there are secluded areas in people's courtyards that might mimic zone 10. I personally have never seen it growing there but that doesn't mean it can't be. It just would require the perfect location. Venice, LA at the mouth of the river and Grand Isle, LA on the gulf both have zone 10 plants growing in situ there. Every decade or so, a real nasty arctic blast wipes out a lot of tropical in New Orleans. It would be worth a try. I grow mine in a pot and it's up against a south facing wall under an oak tree canopy and I never protected it one time last winter, but it was a very mild winter. Only once or twice below freezing and never below 30. Steve