While several other factors all play a roll in powder selection, the primary factor is the "Density" of the shot load. This is based upon the wt in relation to bore size. Based upon this premisis a powder suitable for loading 1 1/8oz in 12ga should be right for 5/8oz in the 28ga & about 3/8oz in the .410.
The "Standard" load for the older 2˝" 28ga shells was 5/8oz shot for which Red Dot would have been emminently suitable especialy considering the "Cooler" paper hulls, & wads. A ˝ oz load would seem an excessive shot wt in the .410 for Red Dot to me.
This is of course all based upon a standard velocity, a high velocity load will require a switch to a slower powder while a low velocity one can be obtained with a faster powder. Some old loading manuals showed a low velocity 12ga load for instance with 1Ľoz shot using Red Dot in about a 3DE loading.