R.P. Case
Lyman 321298 150 grain
Winchester Primer
9.9 grains Dupont 700X
COAL: 2.421
Taper Crimp
F.L. Sized

R.P. Case
Lyman 321317 170 grain
Winchester Primer
9.5 grains Dupont 700X
COAL: 2.450
Taper Crimp
F.L. Sized

Kicks like a Mule. Lighter bullet shot the best.
Original BSA Martini Cadet .310 barrel rechambered to .32 Winchester Special.

Is anyone using the Lee 324 174gr bullet? and Unique Powder?

A martini-cadet action in good condition is a great little action. I have several rifles that use them--none in large calibers. However it has its limitations one is its size. the thickness and the barrel shank make strength an issue with cartridges that can produce high pressures relative to case diameter.
Another limitation is that the curved "loading ramp" top of the hinged block limits the length of the loaded cartridge.  A full length .32 Win Sp loaded with long heavy bullets might be a bit too long to "make the curve". 
 
I like and shoot a bunch of martini actioned rifles including cadets and several larger European Martini-actioned target and "stalking" rifles in larger cartridges up to 7.5x55 Swiss, several 8.15x46, and 9.5x46r Mauser-type cartridge.
Breech-seating bullets for ASSRA-style competition can be a problem if you want to use a mechanical seating tool.  Even an Ideal-type "push seater" has to have a dog-leg built into the shaft and carefully fitted to work with the lengths and angles of the "loading ramp"

Yes. I successfully paper patched a batch of lead pistol bullets that I was given. I recall that the base band was .316 or there about. I have no idea what pistol they were intended for. Gads! that was more than 30 years ago. I have no idea where my loading notes from that era are. I was probably using Unique and not resizing the cases. I didn't buy any special paper. I just used something that was laying around the house. I didn't pursue the paper patch very long. I found an old no-name mold and machined one band off of it to get a bullet that was short enough to stabilize. 

My old eyes are having trouble with the original sights, now. I suppose I could put a long scope on it and offer it on the internet as a rare Australian sniper rifle. I think $2500 would be about right. 

Here is a cast bullet trick that I probably shouldn't admit to knowing. The bullet has to be a semi-wadcutter or wadcutter with a broad flat nose. If you remove the case adapter from the post of a reloading press and screw in a length of 7/8-14 allthread where the dies normally go, you have a simple press with opposing flat surfaces that you can use to squish bullets. The more you squish,the shorter and fatter the bullet will become. Adjust the allthread to give the diameter you want.

Buffalo arms has the correct cadet bullets...a 120 grain heeled bullet.  You can ignore the heeled part and load it with a small dose of unique to give a MV of about 1300 FPS.  That should shoot to where the sights are, and it is a very pleasant round.

The factory loads are not so pleasant, but when used offhand, They are not terrible.

Enjoy.

Ed

I have yet to slug the barrel. What seems to be the norm for these little rifles?