Your proposal would work, as long as your SOA record had short enough TTL's.
It isn't ideal (i.e. it isn't how the big companies like Google, Facebook, etc. manage multi-homed sites), but it is probably the cheapest method.
The other approach would be to host a very small site on Amazon AWS that just redirects... so you have
www.yourdomain.com (on AWS, that then redirects to)
www2.yourdomain.com (in times when your primary ISP is working)
www3.yourdomain.com (when it needs to go to your alternate).
The AWS code could be set to auto-update when it detects an outage, or you could tweak it, and it would have instant effect.
Of course, if money isn't a concern, there are many more elegant solutions -- I did sense that you wanted to have the most economical approach, though.