I can't advise you on rock garden in Texas but I looked through your wish list and recognised some plants ;D
Here is one of them growing in abundance in almost pure quartz sand, Armeria maritima. It also grows in cracks in the rocky outcroppings.
Rogaland, Norway - with cool, often rainy summers (29C max) and mild, often rainy winters (180 cm/year)!
Those Armerias look wonderful in the wild! I have seen the white variety in San Francisco last January and I was amazed by the fact they bloomed in the cold of the winter. I picked one plant, but the problem is that these plants have a very long tap root and when I came home to Dallas I only had pots that were not long enough to contain the root in its entire length... so I curved the root to fit it in the pot, but the plant finally died last May when it started to become probably too warm outside. I think Armerias make such a long root to reach the water way low underground and a pot is not the best place to grow them in, especially where it is very hot in the Summer. In addition, I think the white variety is not nearly as hot-hardy as the pink variety.
Here is a picture I took when I saw them. Yes, I am gonna have Armerias in my garden!
Rino, zone 7/8a Dallas TX, rainfall 38 inch or 1 meter per year (highest rainfall in May with 5.29in/134mm, March with 4.34in/110mm and October with 4.21in/107mm), mild winters with 1-2 days of snow (Record low -1F/-18C) and hot, semi-humid summers (Reco
Your picture could have been taken here in Norway ;)
I would say it is impossible to move Armeias from the wild. As you say they make a extremely long taproot and the root grows into crevices. The plant eventually die if the taproot is cut. I think they are not difficult from seed though.
The other reason why a taproot might be of advantage to an Armeria is that they often grow on cliffs, sometimes pretty solid but sometimes softer shales so the taproot will provide anchorage. A better way than trying to transplant one from the wild, or grow them from seed, might be to take cuttings - they root OK - that's why there are the named cultivars that nurseries sell.
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East Yorkshire, UK