Twigs under 3" in diameter and applied before completely dead are technically called "ramial" wood and are one of the best forms of organic woody amendments to stimulate microbial soil behavior. Better than wood chips in stimulating microbial life.

However, it is important to apply them at a certain age before their decomposition process is completely finished. I'd imagine the store-bought kind is probably too old, but I don't know. The lowly twig is proving highly beneficial.

I'm sorry I am unable to answer your question, though.

Regenerating Soils with Ramial Chipped Wood

Have you looked locally at bulk suppliers? Check the yellow pages under Landscaping Supplies.

Those bulk suppliers will likely offer something called nitrohumus at around $25/cuyd. That is the way to go. They will also have different mulches, some that will have nitrohumus added so the wood breaks down faster.

Charles - I see you're near San Clemente. With that info and a quick google search I found two near you that will probably have everything you need, along with some great local expertise. There is Sierra Soil and Best Soils of California.

What organic matter, yard waste, vegetative waste, is readily available? Leaves from deciduous tress? Shrub trimmings? Grass clippings? There is a wide variety of organic matter that can be obtained for free even in southern California. Many people throw out perfectly good organic matter so they can spend money purchasing something that is not nearly as good at the big box store.
Recycle, reuse.

There is no need to 'remove' any kind of soil unless it is contaminated by something. Clay soil is perfectly decent soil for many reasons that is just sometimes difficult to work or that sometimes drains poorly. Skip adding any additional bagged soil (unnecessary unless you are just plain short of soil) and amend with any kind of organic matter to lighten and improve drainage.

Any of the Kellogg products (and their sister labels, Master Nursery and Gardner&Bloome) will work perfectly well for this purpose but if you need to amend a large area, it will always be far less expensive to purchase in bulk, rather than bagged.

And I trust you are amending over a large area rather than individual planting holes - you want to create a broad uniform texture, not pockets of enriched soil.