OP - I just recently bought my 08 E91 MT. My search took about 3 months ~
I looked out of state and definetely locally with no luck. I worked with an Auto Broker who found one from BMW auction locally last week. Car came from the East coast. Warranty expires next week. Took her in today for check up and the only thing they found was front brakes and they were replaced under warranty. My previous BMW was a CPO E46 M3 and the 3 yrs I owned her had only a door rubber cover loose and some adjustment to my xenons. I believe on the type of engine (In your case N52) you should not worry. Even the service advisor told me today might not be worth it.
As far as finding your unicorn there are out there. I think your budget does not sound too bad but you will find very basic optioned car with maybe some higher miles.
If you are willing to increase the budget you will find her. Just be patient.
I know I only have mine for 1 week but I enjoy the driving experience and look forward to what I will do to her
Cheers