The easiest approach is to buy 310 Cadet brass and the proper 310 Cadet bullets, both available from BACO. Prime and charge the cases, thumb seat the bullets, then fire them. To reload, use a universal decapper and repeat the above. 

Results @ 100 yds:

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I love loading for my Cadet. I have the proper RCBS mold that makes a heeled bullet. .32-20 cases are usable when the rims are swaged thinner. I have the swage and would gladly do cases for anyone who needs them. Return postage is all that would be required unless you want a huge quantity done. A hundred or so would be fine. I tumble lube the bullets with Lee Liquid Alox and when dry I insert them into the the unsized cases. 4.2 grains of Unique shoots to the sights, but your results might vary
Bill

No dies needed for reloading either - at least, not in mine.  Deprime, reprime, charge, seat bullet.  Then fire and restart.  A really fun little rifle and cartridge, pretty accuracte too - if you can manage the sights.  Will shoot well out there, 200 yds no issue - and pretty sure it will do well at longer distances, provided you can read the wind.

I'm very grateful for all of your input. With the help of two great fellas, both Bills, I was able to acquire some cast lead bullets and get some cases made.  One Bill gave me a bag of the heeled bullets cast in the RCBS mold.   The other Bill has a swage in which the 32-20 case rim can be thinned.  The swage is like a .32-20 chamber with a  rim recess to fit the .310.  I gather that he placed a steel or brass block on top of the case head and whacked it to thin the rim. This process  thinned the rim to .065, just perfect for my rifle. The headstamps aren't affected at all.  I gather that the rim gets a little larger in diameter, but it isn't noticeable and it fit my chamber well.     Then I found that I had to trim cases to 1.100 in order to chamber the cartridge. Overall length was 1.600.  The only load I've tried so far is 5 grains of Unique.  The rifle shoots to  the sights and although I haven't fired it for groups, I think it will do fine.   Now I just need to lay in a quantity of bullets.    I used 32-20 Lyman loading dies for loading. Except for sizing the new brass to remove mouth dents, and flaring the case mouth with the expander die, I think I could load it all by hand by just pushing the bullets in the case.  Those archaic heeled bullets are rather useful in that regard.  After the first firing I think that's all I'll need.  What a neat round!  UPDATE:  I can't thumb press in the bullets, but the 32-20 dies work well.  Ultimately I had to shorten the cases to 1.090 for easy chambering.