Transfers between spouses aren’t taxable, nor do they change basis. The gain between the original purchase and the last sale is under $500K, so no taxable gain.
I’m not sure, but I’m guessing that similar rules apply for the purpose of property tax assessments in California. Transfers between spouses don’t generally trigger re-assessments.
And one of the transfers, through a quit-claim deed, wouldn’t be a sale anyway. Under these circumstances, it would be a (probably) non-reportable gift. Gifts between spouses are eligible for an unlimited exclusion.