Can this be salvaged?

I live in Tacoma, Wa, 8b, and due to a very mild winter, my 900 SqFt yard has been decimated by the two pictured menaces.

I’ve already picked up a couple different bags in preparation. For seed, JB Sun and Shade and Scott’s Drought tolerance. As well as starter fertilizer with and without pre-emergent.

I also picked up new sprinklers and a timer for more consistent watering.

I’m thinking if I put seed down once every 6 weeks with some fertilizer, starting in March I can maybe get some coverage back by July.

Is it possible I’m on to something, or is it a fools errand with the dogs around.