Please let's not start beating Dr. S's maybe dead cat over the red shirt again! MT would not have had a red shirt with her on the run when and where she was taken. You give CR too much credit. He is NOT a SK master mind. He did not/would not have gone back to within a couple of miles of his dump site to plant a piece of evidence that could have caused LE to intensify their search.
CR took MT in a moment of opportunity and with a degree of premedation (maybe months, weeks, days, hours, or minutes) killed her, concealed her body and then drove away. He likely spent the last month ignoring the "problem" and looking over his shoulder. He did change his behavior, as at least one store clerk said that he had stopped coming in the last two weeks before his arrest. LIKELY, he was laying low, as when he came into town there was a poster with MT's picture everywhere he turned. Why didn't he run when he had the chance? He had every reason to expect that the body would not be found till fall, and that he had not been seen. Likely, he was in denial about getting caught. If it was his habit to "block out" moments of intense anger, including assault and murder, he might well have blocked out the consequences of his actions, or the fact that he might be caught. The C in CR should stand for 'Cleopatra' as he is the king of denial, not the master of misdirection!