What is the typical bore diameter of the 310 cadet cartridge ?. I am looking at a martini in that caliber and am wondering if it's worth it to brass and bullet mold up if I get it.

With a cadet dies and a mold are the easy part. Brass modification is the hard part unless you have access to a lathe. The. 32-20 case is a perfect start but the rims are too thick and need to be thinned down so they chamber properly. Arsenal molds make a great cadet mold using a copy of the original Greener designed 120 gr bullet. Cadets are fun to play with once you get the brass taken care of I have two of them and enjoy them at the range as they are accurate little rifles even out to 200 meters.

.310 Cadet should have a groove diameter right at .321". 

Difficult to measure as it has odd number rifling.  Should be five groove.

Lots of ways to measure.  Simplest is to measure the slug with a dial caliper. Roll the slug between the loose jaw and watch the measurement that repeats.

I have a V-anvil mic that works also. 

Keep in mid the .310 Cadet uses a heeled bullet it's OD is the same dimension as the OD of the case mouth.

Some sell  a .32 bullet less it gas check as .310 bullets.  This .32 bullet is to long and will jam in the throat.

At one time RCBS sold a proper mould for .310 Cadet.  They may still have it as special order.  I have that mould and a mould  from CBE also designed for .310.  

As Learned from others here on this board,  to lube size these bullets, block the lower feed holes on a sizer die with lead shot and adjust. so lube only get in the lube grove, not the heeled base.