......"then tiller again as needed?" yep you can do that. I prefer to do 90% of the tillering before I cut the bow. Thats just me.
True enough cut it after, but doing it the FG sleeve way you can cut it then realign it. Then build the FG sleeve. You need a good digital caliper to get it perfect or close to.
I built an alignment jig for doing it after the cut.. But like I said before, an FG handle can be a nusiance after when pulling it apart unless you use metal sleeves.