A 540 Skagit head casts well on a TCX 7126. Do not underestimate the capability of that rod to load from the bottom end. I have fished a 510 grain Skagit head but find it a little light.
I enjoy tossing a Nextcast FF 45 7/8, 570 grain floating head on the 7126. The setup just flies. It is also versatile near structure (cliffs, trees, rip-rap rock).
A couple of notes on personal preferences. For longer casts, I like to load the rod into the lower portion. Much of my fishing is from shore and in close so I get to cast off the tip with short casts -- often. I rarely wade out to crotch depth or deeper.
Science is not common sense. Much of it is devoted to a systematic documentation of what we do not know and understand.