You touched on a problem posted on Pianotec in the past; trouble adjusting check without checking on the upswing. As is see it, too much radius (5.25") creates a slow checking sequence. The pianist will have difficulty with fast repetition because the hammer will be traveling in a downward motion (because of slow checking) as the key is returning to rest for the subsequent stroke. Too little radius and the checking is so fast that it creates an undesirable kickback somewhat akin to what we've all experienced when the hammer tail bounces off the top of the backcheck. The unanswered question is: what is the Goldilocks radius and, additionally where is the ideal focal point to give us the ideal checking speed and allow proper checking adjustment, i.e. checking without upward checking. Most manufactures use a 1.5" radius arc, and most important, the focal point. If a 1.5" radius with a focal point placed on the hammer shank line you will encounter removing most the tail because the arc will have started too soon. To eliminate this problem the focal point is placed about 3/8" below (below defined as under the shank while at rest in the action) the shank line.
Another way of looking at this; the back check has only a certain amount of travel within its motion. If the starting point and final checking point are too far apart you will have boxed yourself into a corner with certain keys stick arcs.
I always ask Ray to cove hammers but request that the cove not be deeper than about 1/3 of the moulding depth. Never have a problem with making the adequate radius. Makes it easier to identify front and back of the hammers.
Lonnie, your observations are correct in that manufacturers use a smaller arcing radius than the service industry seems to have migrated into. Many years ago, I was confronted with a repetition problem aired by an accomplished pianist. Upon examination of a Steinway "B" I found that all the regulation specifications were spot on, hammer weight within normal standards, and no excessive friction. But what I eventually discovered, after lengthy experimenting, was that the technician who replaced the hammers used the 5.25" radius and the shank center pin as a focal point to establish the arc. This caused the checking process to become so slow that the hammer was still in a downward stroke when he let up on the key to cycle another stroke. This led me to examine established manufacturers arcing specifications, and I found with Steinway, Yamaha, and Kawai the arc fell between 1 7/8" to 1.5", and I discovered that the arc center-point (focal point) never lied on the shank line. This led me to make my own arcing jig to duplicate the arc radius and focal point of these well established manufacturers.Later, I became puzzled with the claim by some technicians that a larger arc (3" or more) never created a checking problem regarding speed. My suspicion is that the larger arc is not as much a problem with those who install "light" hammers.