Howdy
You can figure out for yourself if the rounds are too short.
Tommygun is correct. There is a small beveled section on the front of the carrier on all 'toggle link' rifles (1860 Henry, 1866 Winchester, 1873 Winchester). When the carrier is in the down position, a round on the carrier prevents the next round in the magazine from protruding out of the magazine. Here is a photo looking down into the carrier of my 44-40 Uberti 1873. The carrier is in the lowered position. Notice the rim of the next round in the magazine is protruding out of the magazine by just about .060 or so (the thickness of the rim).
There is a bevel on the carrier that serves to shove the next round back into the magazine as the carrier rises. This is the carrier of my Henry, but it does not matter, the carriers are designed the same way. Just as they were back in 1860. The arrow is pointing to the bevel. If a round on the carrier is too short, the next round in the magazine will protrude just a little bit too far and the bevel will not be able to sweep it back into the magazine so the carrier can travel all the way up. Since your rifle is chambered for 357 Mag, the bevel has to be long enough to be able to compensate for the shorter 38 Special rounds. Those dummy rounds of yours might be just short enough that they allow the next round in the magazine to extend just a tad too far. The fact the going gets easier when there are less rounds in the magazine suggests to me those rounds are right on the hairy edge of being too short. With less rounds in the magazine, the magazine spring is not shoving the rounds back with as much force, so if a round is right at the edge of the bevel it might be easier to shove back into the magazine.
It should be easy enough to determine this yourself, now that you know how the action works. Shine a bright light down onto the carrier and watch what happens when you work the action slowly. If the protruding round snags against the flat surface of the carrier, there's your answer.
By the way, the correct name for that bullet shape is Truncated Cone, not Flat Nose.