Since her appointment in April 2004, Rachel Moore, a former dancer, now 41, has taken firm hold of an unwieldy, creaky organization that is also a great one, constantly beset by financial problems, yet somehow managing to produce the spectacular productions and dancers for which it is famous. Since Ms. Moore took over, Ballet Theater’s endowment has risen from $8 million to $15 million; its City Center season this fall showed box office gains of 30 percent over the previous year; and for the first time in six years, an operating deficit has disappeared and a modest surplus is projected when audit results are released next week.