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Yes, you may do that. You can also harvest the seeds, as they are really easy to germinate. Either way will get the results you want.

Soil improvement is fundamental for plant health, so you are on the right track by adding topsoil. You can also improve the native clayey soil by incorporating compost or an enriched organic potting soil to increase soil organic matter content. Mulch the soil surface with the same.
https://www.domyown.com/dr-earth-home-grown-organic-potting-soil-p-9497.html

Soil testing and recommendations for mineral amendments based on actual deficiences found is the best way to go, or at least use a complete organic fertilizer like one of these:

http://www.soilminerals.com/Agricolas4-8-4_MainPage.htm

https://www.domyown.com/dr-earth-organic-all-purpose-fertilizer-p-9485.html

The most consideration is to buy a native coneflower. These are the plants that have adapted to your area. The same plant from a different region will have slightly different characteristics. Here are two websites to help you out: https://npsot.org/wp/houston/go-native/
https://www.wildflower.org/plants/combo.php?fromsearch=true&distribution=&habit=habit_herb&duration=duration_perennial. This page is for East Texas. On the right, you can change the search terms if you wish. Several coneflowers are listed (Echinacea). Click on a plant for more information; near the bottom of the page it tells you where you can find this plant or seeds.

I would only water the ground is dry down to two inches. If you feel moisture within this area at all, then it would not be a good idea to water. Coneflower are very drought tolerant, but will not tolerate wet soils for very long. Most grasses can handle some dry spells, so to be on the safe side, you will only want to water when it is almost completely dry.

It is common for coneflower petals to fade to a light pink as they age. There are coneflower hybrids that bloom a true white. I suppose it is possible that your coneflower is from seed that was cross-pollinated with a white form. As prolific self-sowers random mutations or "sports" are also possible. If you are seeking a deep purple color, buy a new plant. Unfortunately, there is nothing you can do to change the color.

Birds that are eating the seeds can make a mess of the petals, too. You would probably see them, though. Japanese beetles are always a threat as are earwigs and even rabbits. Sleuth some more in early morning and evening, or go out at night with a flashlight to find the perpetrator. Here are some solutions:
https://www.gardeningknowhow.com/ornamental/flowers/coneflower/coneflower-problems.htm
https://ask.extension.org/questions/350115