You *may* not need to refi your VA mortgage in Washington if you wanted to use your VA benefits to purchase a home in San Diego using a VA mortgage - it depends on how much entitlement you have remaining.
As you know, VA mortgages can do 100% financing, so if you were looking to put as little money down as possible then VA certainly would be a great option. Even with owning another home with a VA mortgage, you could still get another VA mortgage as long as you have enough entitlement - have you requested your Certificate of Eligibility? You can do so online at https://vip.vba.va.gov/portal/VBAH/Home
(click user registration on the left if you haven't already registered).
To start, realize that the total entitlement (basic & 2nd tier) is $104,250 in areas that have the normal VA loan limit ($417k). That is the basic entitlement of $36,000 plus the 2nd tier entitlement of $68,250. This represents the amount of the mortgage that the VA guarantees. On a zero down loan, lenders require VA to guarantee 25% of the loan amount. So on a sales price of $144k, the VA guarantees $36,000 and the lender has no problem giving you 100% financing. However if you buy a home above $144k, and still want to 100% financing, it's still possible to do by using your 2nd tier entitlement amount of $68,250, which together totals 25% of $417k and is the VA loan limit in most counties. FYI, the total entitlement in areas that have higher than $417k VA loan limits is 25% of the county limit.
So hypothetically in your situation let's say you only have $7,680 of basic entitlement remaining, which translates to 25% of a $38,400 sales price you could get 100% VA financing on. You may have your 2nd tier/bonus entitlement as well (call VA to confirm). $38,400 probably won't get what you need... so you would need to use your 2nd tier entitlement. The trick is that in order for the 2nd tier entitlement to kick in, your new loan needs to be over $144k.
has various examples of how to use the entitlement for a VA mortgage guarantee. Example #5 would be similar to your situation.
Hope this has helped and if you need further help let me know!