I forgot to mention that I'm in Southern California

Compost will fix soil texture. Potting soil won't do any better, and is a lot pricier. As to nutrition, I'm skeptical that you can pronounce your soil poor nutrition-wise by just looking at it. Get it tested. But if you don't want to do that, then you might just hit it with some broad spectrum fert like Miracle Gro. That's the shotgun approach. Boom.

P.S. It is rumored that eucalyptus is allelopathic, which means it exudes stuff that kills plants. You might look into this. It may be selective allelopathy, wherein it kills some things but not others. Might be wise to see to it that no roots remain, and maybe that all previous leaf litter is removed as well. Of course, eventually, as the eucalyptus remnants degrade, any such allelopathy will eventually go away.

I would mix in some garden soil, and maybe a bag or two of soil conditioner. Some 10-10-10 fertilizer couldn't hurt either. Just for the grins, a soil test would be fun.

you can buy organic coco bricks for pretty cheap ($12/brick here) and they are excellent for adding aeration to heavy/compact dirt. 1 brick when expanded is enough to fill a wheel barrel, 2-3 bricks should be enough for a 4x10 area, superior alternative to peat based potting soils.. add compost and a few bags of worm castings/manure.

use organic fertilizer which helps with conditioning of soil (fish emulsion,etc). in the fall, save leaves from trees and turn them into leave mold. they can be used as mulch which will break down into the soil which also feeds and attracts microorganisms to the soil (earthworms,etc) which all contribute into conditioning soil.