Well..... sometimes ya gotta ‘scratch the itch’. I did what you are thinking about: bought a Handi in 30/30 Win and reamed it to 30/30 Ackley Improved, main reason being — I WANTED TO.
A few notes: I have several gunsmithing friends with about every tool and machinery you might imagine. A 30/30 Ack Imp reamer was easily borrowed from one that had done a few jobs. FIRST you measure the headspace in your rifle with a no go gauge to check it for correct factory setting, as some are rumored to be sloppy. Then you insure you do not create extra headspace when reaming your AI chamber by not cutting the case rim recess ANY deeper than it already is from the factory. This headspace on the rim is important for the first fire forming of standard factory ammo. Subsequent firings will use the AI case’s shoulder, not the rim.
30/30 Ack Imp dies are available from Lee Precision as standard pricing probably because they are the most commonly requested Ackley dies from the public. Midway USA used to offer them for ‘normal’ standard die set prices.
There is one other option: use a 308 Winchester Full length sizing die and of course a 30/30 shell holder. This setup will size part of your 30/30AI case’s NECK, with plenty of bullet hold tension for a single shot rifle. I did this, thinking I would buy an Ackley die set when my cases finally needed full resizing, but,... they never did!
I had extremely good accuracy out of my Handi 30/30 barrel both before and after reaming. I easily killed two deer seconds apart at about 65 yards, taking my time to reload. A single shot should not be a deterrent to successfully harvesting even multiple deer.
I loaded Nosler BTs using IMR 3031 powder and got excellent accuracy.
Let me finish with this: Don’t try to make your 30/30AI a 308 Win. Enjoy it with recommended load data.
Is it ‘worth it’? To most shooters maybe not. 30/30 cases are usually easy to find, so extended case life isn’t a good reason for AI’ing. Others posting here have some good reasons for reaming to other cartridges OR, leaving it a standard 30/30 Win, not a bad thing!
Enjoy scratching the itch.
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Note: REreading your post you mention the Handi you have is OLD. I would have it carefully inspected by a competent gunsmith as some of the old Toppers were or became a loose fit with lots of use.
Also, Midway USA shows Lee Pacesetter die set for 30/30 Ackley for $36.99.

Last edited by Alaninga; 08/11/19.