Your blend is half organic matter, not counting the organic component of the topsoil. Not only may this aspect be causing excessive drainage but when this organic part of the mixture decomposes and disappears - something that can happen within a year in a hot climate like yours - there will be associated shrinkage and settling.

The Myth of Clean Compost

https://s3.wp.wsu.edu/uploads/sites/403/2015/03/clean-compost.pdf

The Myth of Soil Amendments - Part III

https://s3.wp.wsu.edu/uploads/sites/403/2015/03/soil-amendments-3.pdf

You say "the soil is bone dry" a day later. You mean the surface? No problem. That's what my soil does. You're not in a climate that will keep the surface moist. If it's bone try an inch or two down a day later, your organic content may be provoking excessive drainage, and allowing a lot of ventilation that speeds evaporation. That's where the roots of your plants are. Very true about shrinkage. That compost will disappear as it gets degraded by soil bacteria, as will the peat moss, a little more slowly. Be prepared to keep adding to the bed. Also true that it's really hard to "wet" organic material. It sloughs off water when dry. So some patience may be needed.

How are you watering? A slow watering using soaker hoses or drip irrigation a couple times a week works better than a short daily watering. When I water my raised beds I use a soaker hose on the lowest pressure and water for 1-2 hours. With well mulched beds once a week is usually enough even in the peak of summer.

In terms of what you can do now, mulch on top, slow watering. The mulch will also go some way to helping with the shrinkage.

I'd pop out the transplants and replace the contents of the bed with something that is going to work out better. Something that has a much lower percentage of organic material (see discussion at my second link).

With raised beds, the percentage of the organic matter is far less of an issue than it is with inground plantings. The links provided above address inground growing, not raised beds, and other than the shrinkage, the quantity of OM is not a concern. Certainly not a sufficient reason to remove all the soil and replace!!

Lasagna gardening is essentially gardening in 100% organic matter and is a highly successful and well known method!!

With a decent mulch and low, slow thorough watering - drip or soaker hose is excellent - you should be fine.

Ashley isn't gardening in an isolated pot or tub on a patio, they are gardening in a raised bed. One where they have already included a component of soil, because successfully used raised beds are made of soil on top of an existing grade. And because an existing layer of soil is involved

I also tilled underneath about 5" and mixed in some native soil as well.

With the excessive amount of organic matter likely to be the cause of Ashley's watering problems. And the cause of other difficulties later, including shrinkage, settling and soil mineral content issues. With the latter perhaps soon to appear.

Never said or inferred it was a pot - a raised bed is a raised bed and is NOT the same as digging a hole and planting directly in the ground!

That is exactly the way raised beds are used........imported soils and amendments mixed with native, mineral based soils. !00's of thousands of gardeners do this exact same process every year and with great success. It is not reasonable to assume Ashley will have any less success with her methodology!!

People have been known to grow vegetables in 100% compost successfully in raised beds. And that is far more of an instance where excessive OM could be - but really isn't - a problem.

btw, additions of organic matter are typically advised to increase water retention. It is far more likely that the OM was not sufficiently hydrated before adding to the soil mix, which could account for the hydrophobic nature of the soil mix now.

A note on this (partly as a question as I'm not certain) - I believe soil organic material is measured on a dry weight basis, but I'm guessing most of us would intuitively estimate the amount of compost and peat on a volume basis, or at best rough weight. Since OM is both lighter (lots of air inside) and often contains quite a bit of water, either will overestimate quite significantly the OM compared to what a proper soil test would give. Perhaps someone has a correction factor, but as an educated guess, that might mean the OM is 20-25% (restated in dry weight terms), possibly even lower. That still might be higher than the typical recommended levels but probably not significant (esp if that OM will decompose quickly).

My personal opinion is that it would be a waste of time and effort to redo the bed entirely, just mulch and water carefully and see how it works out.

I added some of my worm castings to some of my mixes that seem to dry out and as a result they seem to absorb water more easily and hold onto it longer as well.

If you do not have a soaker hose at least measure the amount you are putting out. If you have a water can water as slowly as you are able. You should put out as least 5 gallons of water on a 4X4 to wet if the soil is dried out. The roots will eventually go deep and get the lower moisture.

When you first put out transplants they will probably need to be watered daily. It takes time for the roots to spread out. After a couple of weeks the roots should be deep enough to get down to the water, especially for tomatoes.

Peat moss repels water indefinitely if it's not pre-moistened prior to incorporation into the soil---according to my mentor, Thalassa Cruso, circa 1974.

It is only 20% peat moss. As long as it is mixed well, it will get wet. Otherwise, how could the peat moss bales get moist at the store. The top ones are usually heavier due to getting wet if there is a hole.

If there is a big chunk or thick layer, then yes, would be very hard for the peat to take on water. That usually occurs in a potting mixes that is well over 50% peat moss.