I don't have these calipers, but I've been thinking about them. I haven't read the installation sheets either.
So take this as speculative.
From what I've seen in the sales material, the calipers are compatible with both older (flying shift cable) Shimano levers and newer (9000/7900/6800/6700/5700 under the bartape shift cables) Shimano levers.
These two lever types have two different cable pull ratios. From what I've read, the TRP HY/RD accomplishes compatibility with either lever by means of having two different cable anchor points. Your experience sounds very much like using newer levers with the older brake anchor point. (Done the opposite way--older levers, newer brake anchor point--should fling you right off the bike with a light squeeze.)
Again, don't consider this authoritative.
I don't own them and am going only by the sales material I've seen. But it's something worth looking into, at least so that you can check it off the list.