The only AI conversion I would think about in a Handi would be a 30-30AI.
And even that would largely depend on the existing chamber and how the rifle shoots in the standard caliber. The Handi's have too many loose connections and accuracy is not one of their strong points in many of them.
So forget about AI conversions, another downfall with an Handi AI conversion is that you cannot set the barrel back to clean up the chamber and get a .004" crush fit for fire forming.
Unless you use a larger/longer case. From my experience with the Handi, more power, more back pressure means more inaccuracy. This of course is not the case with in a 30-30AI, besides the rim keeps the head space without the set back. In some rifles the lock up is so bad the action will open when fired, and many will partially open when full loads are used.
It also has been noted that the smaller case heads and the lower presuure cartridges perform much more satisfactory. IE, 22Hornet, 223, 30-30, 38-55, 45-70. 44Mag. 357 Mag. I know for a fact that some will argue this point. Fred M.