I have been reloading 44-40 since 1971. I have done all the above except anything that has to do with any metal removing or reaming. As you said, the cylinder only 2 chambers will load, the other 4 will not. The cylinder chambers are not the same, that is a defect. Check the cylinder with as factory round to see if they fit, drops into all the chambers, and drops out, if not send the gun back. I had an Uberti that even factory Remington 44-40 JSP (.427) won't chamber in all the chambers, without pushing them in, and using ejector rod to remove the ones pushed in.
I use a second generation cylinder I got from Dixie Gun works in 1972 as my test cylinder.
If I were you I would size 1 brass, check to see if it fits in all the chamber, do six, check all, do 12 check the last six, if all fit, do 50 check the last 6, then even 6 out of 50, or until you are sure sizing is done correctly.
Make a dummy load with bullet size you going to use, the dummy load should drop into each chamber and drop out, if not try the next size down, .429, .428, .427 until it does. If .427 doesn't work it is the gun.
I have old reloading equipment a Lyman ALL American Turret Press, and RCBS dies, all purchased new in 1972, and I check first several loaded rounds and then 6 out of 50 for size. Sometimes I have to a adjust the press, usually I can load 80-90 an hour, checking the powder weight every six round on a electronic scale.
I hope this helps you.