I fear that rental pricing in the core will soften quite a bit (going to get very competitive to attract quality tenants and fill vacancy).

Like everything else in economics, it depends.Many real estate investors (those looking to buy) were longing for the market to cool, in order to see some softening in prices and better cap rates. 

Then my question to you is, do your final numbers still work for a BRRRR if you pay the higher price, do get a lower sales ARV, and rents soften? 

In fact, I would expect more softening in residential multifamily in the coming months as CA's eviction moratorium is extended and mom-and-pop landlords decide to call it quits.Also, with $150K and a 10% down loan in Orange, you can definitely afford to get in the market now.

@Joseph Cameron absolutely no softening here.

When the market starts to soften, often those are the properties that slow down first. 

Refinancing to new 30-year fixed (would be 2.85% w/ 6100 closing costs rolled in), with the goal of buying a new house and renting the condo out in 6 months-1 year when/if the market softens.

Here is my take:   With key parts of the economy is disarray, I expected the real estate market to soften up a lot.   

So much for any hopes of a Covid softening in prices. 

It is my opinion that when the new inventory hits the market, the market will soften slightly and go back to a healthier growth rate.