Two years ago, investors handed veteran oilman Jim Hackett a $1 billion check and sent him to seek riches in shale drilling. Today, the company he founded with their money, Alta Mesa Resources Inc., has a market value of about $43 million and is teetering on financial ruin—one of the more spectacular failures met chasing the next big thing in the American shale boom. Mr. Hackett bet big on an up-and-coming Oklahoma oil field after early wells there rivaled those of the best fields in Texas, but subsequent output has been disappointing. …