Unless the coil shows really obvious signs of a meltdown, it's almost never the coil. If it's activating (and subsequently stuck on and buzzing), then that suggests a stuck switch upstream from it that's controlling the logic.
An M29-1000 will have 100 fewer turns though, so will have less resistance and run hotter. Looks like some used M29-1100 are available though:
http://user.xmission.com/~daina/parts/parts_for_sale.html
(search for 1100).