OK Tim,

As a recruiter i only deal with reputable schools and can only quote for the schools I deal with. All are private schools that supply an education to pupils from Kindergarden 2 up to grade 12 (pre school to pre university)
Schools that pay over $1,000 to my knowledge:

Sarasas Afiliated schools have a pay structure that starts at 33,000 baht ($868) but rises up to 60,000 baht ($1,579) with experienced teachers.

Udom Suksa School salary starts at roughly 35,000 baht ($921) and is negotiable after passing probation. Second year is much better pay, you are rewarded for loyalty.

St. Francis Xavier school starting salary at 40,000 baht ($1052) plus extra for experience.

There are other schools as well, but I'm a bit pushed for time.

As a suggestion read:
http://www.wwedu.net/TeachersWorldwide/TeachinginThailand.htm
It can help youdecide if you really want to come to Thailand.

If you want any more help email me

Yes Tim, Thee are several schools paying over $1,000 per month in Thailand, and with your speciality, ther should be no problem in your getting a decent job.

By the way, $1,000 is now about 38,000 baht, not 45,000, big difference, about the same as a Thai teachers salary.