Well, I will share what I know however I am without a .30-30 at the moment.
First let me address the extraction question. I understand that the rimmed cases dont usually suffer from the sticky case problem and the .30-30 has s rim so that should take care of that problem.
Next, it is my opinion that while spitzers can be fired in a single shot I would hate to have someone accidentally load one into a tubular magazine and shoot the rifle. My thought is to ream out the Handi to a .30-30 Ackley Improved therefore making it impossible to fire in a regular .30-30 chamber. Then too, the increased shoulder angle slows down case stretching and the added case capacity gives about 200-feet per second more velocity. As an interesting side note, Ackley discovered that since the modified case griped the chamber walls better and the case head diameter had not been increased or altered, the rearward case head thrust was actually reduced on the breach face even though the velocity was higher. Also, if you neck size only that too will cut down case stretch.
In theory less rearward case head thrust should mean a slight reduction in felt recoil as well. Probably not enough to feel but you will not be straining the action at all with that extra bit of velocity.
Also, any Ackley modified chamber can still fire factory .30-30 ammo so if you run out of your handloads you can get a box of regular shells and keep on shooting. After all, that is how you fire form the cases anyway. And if you are planning to shoot spitzers you are handloading anyway so handloading for the AI should not be any more trouble.
In addition, the extra little bit of velocity means you will be better able to take advantage of what those spitzers have to offer.
Lastly, reaming out the chamber to the Ackley Improved is an easy hand operation. No different than when a bunch of shooters here reamed .357 Magnums into .357 Maximums.
I probably didnt answer your questions as you wanted but hopefully I gave you some food for thought. Do a Goggle search on the .30-30 Ackley Improved and read what others have had to say about it. My next .30-30 will definitely get the Ackley modification.
PS: I hear that the regular .30-30 works great and is accurate in the Handi if that is all the farther you want to go.