How to repair shower p-trap
The procedure described is accurate. 

My advice:

Hire your plumber (or a different plumber, if yours doesn't have the equipment) to inspect the drain with a camera to confirm that the trap is the only part of the drain that is damaged. You don't want to dig up the trap only to find later that there are additional issues and you don't want to do "exploratory surgery".

If you wanted custom candlesticks you would not hire a butcher or baker, you would hire a candlestick maker. Have a tile professional give you a bid on the job, for re-tiling and repairing (or replacing) the shower pan and tile, explain the reason and have him/her include excavation and replacement of the trap and drain assembly in the bid.

Done correctly you can just replace the floor and lower wall tiles (the "pan"); most folks choose a contrasting or complementary color and tile style and it looks ok. Be advised that this involves some waterproofing steps and it is not a simple job. Tile pros  are usually very competent with the plumbing associated with the shower; they know best how to set the trap and drain assembly to ensure that it is at the correct height for the finished tile surface. Have them include everything in the bid.

Alternatively, have your plumber give a bid on just repairing/replacing the trap with it already chipped out for him/her by the tile contractor. The plumber should work with the tile contractor to ensure the drain and stuff will be correct.

Note: prices for services are off topic here. Always hire through personal references, always hire reputable licensed contractors, always get multiple bids (it's ok to be honest and tell potential service providers that you are getting multiple bids).

P.S.- I live in So Cal and had my entire sewer main dug up and replaced (6' deep X 50' long) for $6,000...