Ideally, you would have the butcher do it (with his bandsaw, he stands the loin on end and makes one shallow cut (about an inch into the loin), just enough to separate the ribs from the chine (you're cutting through the ribs, not the chine). He may have to turn the loin from bottom to top then top to bottom (rotate it) so he can get the other half done. In all likelihood, the bandsaw head can't be opened tall enough to get the whole loin in at one go.
Then, when you get home you finish the cut by cutting along the chine/rib stubs. Lastly would be you making a cut following the rib line from top to bottom. You'd end up with:
1)back ribs with however much meat you left on them when you did that final cut (cut ribs off the loin)
2)boneless loin roast
3)chine (with rib stubs attached). You can further trim this to get those little morsels between the rib stubs. Although there was another thread about people asking what to do with the chine, IMO cut what little meat is left on that bone and toss the bone.
Failing that unless you have a meat band saw, your only alternative is to leave it in place. Or cut around the rib then the chine then the rib then the chine, etc..Not a viable solution.
Bottom line is you have to cut
through the ribs (very close to where they join the chine) to separate them from the chine.
Get your butcher to do it.
edit: This video
goes about it slightly differently but catches the sssence of what I described. Whereas I only make that 1" deep cut (IMO, I leave more meat on the loin doing it my way), he cuts the whole chine out in one swoop. EIther way will work. Only the first minute relates to your question.