I was thinking of shrinking it in with dry ice on the insert and heat on the barrel at about 0.0015" interference per 1" diameter at ambient. Maybe with hydraulic press assistance- I have access to all of these.
The rule of thumb is 0.001" interference per 1" diameter. My calcs say it should slip in at 0.0015"/Ø1". I've seen 5 thou on 3 inch interference fits (.00167"/Ø1") so it should go.
What would be the advantage of threading in over shrinking?

My reasoning for shrinking is a couple of posts on another forums gunsmithing section in which a member, who seems quite well respected by that forums other members, describing his process for shrink fitting an insert.
I have assisted in some shrink fitting (bigger stuff) and it's unbelievably strong.