I think most all of the discusions about rods need to be pre-qualified by what kind of fishing they are used for. It has been so long since I've done any trout or landlock fishing in rivers and large streams I have no way to compare, since over 90% of that was done with either an 8 foot Leonard Duracane 6wt or a 7 1/2' Gene Edwards varnished 5 wt cane rod. I did later buy an 8 1/2' Sage RPL for bushwacking, but preferred cane to it.
Now, since fishing nothing but salt, and ocassional bass, I like to stay as far from the fish as I can reasonably reach. And from that perspective, rod action is less important to me than the rods overall power when really loaded with line.
I do not think rod action makes alll that much difference when really loaded. I've seen pictures taken from videos of different rod actions when heavily loaded for distance casts, and cannot see much, if any, difference in the bend across the board of action types. In fact, comparing stills taken from a vintage film of a world class distance champion from the 50's using a glass rod, I could determine no significant difference in rod bend from his fiberglass rod and my TCX on a long cast.
So I think rod power trumps action type for distance casts.
I haven't tried as many rods as I would like, and haven't taken the time to do any static testing of them like hanging weights on them and so on. The nicest casting rod I have ever cast, and which felt unbelieveable to me at the first cast was a Sage TCX 7 wt (with the silver reel seat) using a 7 wt line. I also like the 8 wt TCR with a 7 wt line. My daughter, who sadly has very little time on a rod handle, preferred the Sage TCR with an 8 wt line to the TCX with a 7wt line when casting them side by side, switching back and forth - but it took her a number of switches to decide.
I recently bought a 12 wt Sage xi3 and cast a 12 wt Rio Tarpon floating on it, but I like my late 1980's Sage RPLX 12 wt better with that line. From what I've been told, that old 12 wt was the most unpopular rod they ever made. Typical. However, I think the Xi3 will be perfect with an 11 wt line. That is what I was after anyhow, a powerful 11 wt rod.
When casting the TFO Ticr and Ticrx, I thought they were underpowered for the line ratings. To me they felt too soft in the tip for long casts. It felt like I was wasting too much at the beginning of the stroke in bending the rod and not getting the line moving.
For that kind of casting, I only use one casting stroke, as long as I can get. The tempo of the stroke changes, and the timing of clamping the line changes and the haul changes, but the total arc length doesn't change on the presentation cast (depending on the definition of casting arc length).
Since there are an infinite number of factors and degrees involved in casting physics, and and infinite number of casting styles involved, and an infinitely varying amount of feedback reaching the caster during each stroke, I think it's not possible to arrive at any generalizations at all.
Sorry, after all that typing, I can be of no help, Pegboy, and know less than what I thought I knew before I started.