Might want to give Cameron at Craft&Tailored a call. He is also in Los Angeles.
He has a couple moderns within your price range along with a slew of vintages.
https://www.rolexforums.com/showthread.php?t=528839
https://www.rolexforums.com/showthread.php?t=530294
I bought a 5513 from him. Cool guy, he also showed me a few of his other cool vintage pieces also. Highly recommend.
Chris
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