Why would you have any financial hardship with a 360K stash?
The possible scenario's
-no market crash, both working: great, stay the course!!
-no market crash, somebody gets fired: meh, you have a 360k stash, you can take your time and find new employment.
-market crash, both working: nice, more stock at a cheaper price, keep saving, keep investing
-market crash + unemployment: even a very bad crash would leave you with a stash of around 180k. That is still plenty to find employment + since you are renting you have the flexibility to move to where employment prospects are better
If you really want to own a house: find a fixer upper that is good value (look long and hard), put 10% down, take a mortgage for the rest (rates are still pretty low) on 20 years and make the regular monthly payments. Build up some sweat equity in the house. You will be adding value to the house on the cheap since you do most of the work yourself. This way, even in in a crash environment you will still break even (might lose the sweat equity, but hey it's sweat equity!). And you also acquire skills that can help find a job if you lose current work.
On the plus side, you will be so busy with the renovation you won't have time to ponder what might or might not go wrong....