First and foremost, there is no one size fits all model.

Depending on the vintage, size, condition, etc you're going to be hard pressed to find something for $12k a unit.

Curious, what size MF property are you looking for?

Find similar sized homes, and calculate the price per sq ft of each.

Check with the planning department to get an idea of the review time. 150-180 $/sf seems low for "high end" on the west side of LA.Based on the size of the house you may not need an architectural stamp, even if you are adding a story.

They are easier, albiet hard, to find than a larger apartment complex in the area and will offer you a good introduction into property management before you bite off a big chunk.Like Matthew mentioned you can also do conventional or FHA financing on these size units.  

Sounds like a full gut rehab job or tear down and rebuild with that size budget. 

You can make minor adjustments based on the type of appliances (dishwasher, clothes washer and dryer, air conditioning, etc.) and the size of the rental.

So I could put the house back on the market after that, though I would take a decent size "loss".

I certainly do think there are opportunities to be had in the > $10M deal size.