Your young appear to have a lot of ornata influence. They are very pretty! Nicely done. Also, further proof that young turtles will willingly accept vegetables! This seems to be especially true of Three-toeds.
Many people keep Easterns in various areas of Texas. I have spoken with a few Texans in the past, and most of them have had to install drip systems in the outdoor enclosures. Houston is pretty wet compared to most of Texas, but still a bit on the dry side for true T.c.carolina, or bauri, or major. The drip system is used to keep the soil moist, and a weekly soaking (about an inch per week) with an overhead source is a good idea, whether by rain or garden hose.
Also, it would be a good idea to amend the soil with a lot of organic material, especailly peat. If I am not mistaken, the pH of your soil is pretty high (basic). Easterns, Floridas, and Gulf Coast box turtles seem to do better in slightly to highly acidic conditions.
I emailed one "acquaintance" after reading your first post on this question. He lives near Amarillo. He makes no effort to increase the "wetness" of his Eastern subspecies' enclosures. He said that adults do well with a deep pile of compost that he keeps wet by spraying periodically throughout the summer and especially the winter. He has to maintain juveniles indoors as they will "dry up like raisins". Also, if he doesn't catch a female in the act of nesting, the eggs will be nearly completely dry the following morning. His turtles have a lot of eye problems. I have talked to him about that before...it could be dietary, but is most likely related to humidity. He also said that his ornates will catch their own food often, but the Easterns are too slow to catch the native insects for the most part.
If it were me, I'd take a few more precautions.
I hope this helps. Good luck.