No way, the point of a no mow mix is so it doesn't look like an abandoned crack house with out of control grass there. There are groundcovers that grow slowly in height so that it does not look like the property is not maintained! Irish moss! This is the first year I'm growing creeping red fescue which I know is popular for unmowed hillsides but this grass grows like a mother. I wouldn't want to use it somewhere that the lovely plumes of long grass would bother me such as in a small yard. Just too fast. Now I have a blend of dwarf tttf that is used in "LOW-mow" and it actually does grow really slow. It hasn't needed mowing hardly at all and stays short.

Just my experience, but... 1. Yes, it will grow back if you simply overseed 2. Depending on the type of grass it is, rototilling and picking will likely not be sufficient. Ive spent the last year trying to eliminate the stuff, and am only now feeling like Ive gotten ahead of the problem. One polite suggestion: dont plant grass. Find some other groundcover type of plant to put there. Grass just isnt a good idea here in AZ, uses too much water and needs fertilizing, pesticiding, etc. Try sweet potatos. The kitty will appreciate the hiding spots, and it can be manicured and kept looking good without so much additional chemicals.

You won't need starter when you overseed, and the new grass won't need a thing for at least 30 days after sprout (seed contains the first month of every required resource). At the 1 month point, feed gently with a nitrogen-bearing fertilizer, or feed with an organic grain-based fertilizer when you plant (it'll become available at week 3 to 4). Watering...I'd play it by ear, but given your sodium levels, I'd still go with the full inch until those go down. We really don't want to make that any worse, which shallow irrigation will do.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.