My preferred approach is to use the excellent PTG bottom metal (which is approximately $100), and send your existing stock to a gunsmith for inletting. The PTG bottom metal fits the Badger M5 inlet, and the geometry is fairly complex. While the work can be done at home with any number of tools, this is a case where it's probably best to spend another $75 for professional assistance (and this is coming from someone with a machine shop in his pole barn, so I've been there and done that). If the inletting is performed cleanly, there should not be a need for any additional stock work such as bedding, although it probably wouldn't hurt.
The toughest part of the project will be finding an Accuracy International magazine for .223. They are presently rather difficult to acquire.