The Assessor is required by law to assess all real property at current value, which is represented by the replacement cost of the improvement less depreciation and market value of the land.

I am handy and will replace the handle myself. 

I moved in and immediately replaced all of the carpet flooring in the house with engineered hardwood; I re-painted the entire interior; I replaced all kitchen appliances with new ones that I found at a discount at an outlet/scratch and dent; and replaced the water heater.

It was such a cheap property ($50k), I didnt bother depreciating anything.You could ask your insurer for "replacement value" insurance (Since you probably want that anyway unless you would leave any burned down buildings unreplaced.)

Once we replace them, it’ll go up to about 50% COC. 

We upgraded the bathroom and kitchen floors, put up newer cabinets in the kitchen, and replaced the washer and dryer with newer (used) ones.What was the outcome?

Recently, I put 10K into roof repairs and I'll have to replace a kitchen soon.

Assume 600 sf to be replaced every 10 years.

Is an overlay as good as a full replacement?

The cash and the note must somehow be used toward the purchase of your replacement property if you want to indefinitely defer all of your taxes.