every state is different, check yours before you make a decision.The original title would have to stay with the oem frame. If you sold it, the title would go with it. It's not any benefit to you to "keep the original" title once you go special construction. The aftermarket framed bike will have it's own title and the original title would be useless to that bike because the frame numbers wouldn't match.
Chop yours- the title will remain as is.
If you get aftermarket, you may have to get a "built" title or just use your own and keep your frame at home.
Get a pre-number frame and chop it - use your title or built title
get after market- graft your numbered neck on keep your title
get aftermarket- stamp your numbers on it and keep your original frame (hidden)
it's not against the law to restamp numbers- it's only illegal to alter them
Although sometimes it takes a judge and a couple of lawyers to decide