Are there any opinions on whether it's best to use a taper, plug, or bottoming tap when cutting the threads to pull a 3/8" sleeve bolt? Passes with all three?
You'll probably have better luck with the taper or plug than the bottoming. The problem with removing rusty 3/8" sleeves is that they break apart, and the bottoming tap will have a full-depth thread at the junction between untouched sleeve and newly-threaded sleeve. The plug may or may not lead with a shallow thread, but the taper probably will have one or two gradually deeper threads. That may give you better purchase without tearing the sleeve apart.
One tip is to re-tighten the draw stud into the sleeve several times during the pulling process rather than just hoping it will slide all the way out.
Yeah I like the idea of snugging the draw stud onto taper-cut threads but I didn't know if there's enough purchase there.
When you say re-tighten, do you mean remove the draw stud and cut more threads or just tighten it by turning? Is this because the draw stud bottoms out on the cone at first? Is there any risk of hooking the cone threads with the 5/16 tip of the draw stud?
I mean rotating the draw stud to screw it deeper into the sleeve. Even if the threads at the tip of the draw stud ride up onto uncut rusty metal, they still have a little bit of bite. Any purchase you can get on the uncut portion of the sleeve is likely to help to extract it without tearing it in half.
I usually cut just 5 or 6 threads in a sleeve that is ~1.5" long, so hitting the cone is not common. I have tapped all the way into a cone before when demonstrating removal with a really short 5-piece bolt. The draw stud just pulled out the sleeve and cone at the same time. I wouldn't make that a standard practice, tho - it was more tapping than necessary.