By George, I think I've GOT IT!
See photo attached.
I did not at first want to do it this way, but on a lark or by happenstance, I subconsciously was after something else and this hit me right in the face. I think it is my solution, avoids trimming, no need for mirroring, and should speed things up DRAMATICALLY!!!!!
-- Project the profile onto the surface
-- build between the lines the surfaces making the web and flange
-- use the solids tool One Rail Sweep Surface to project the surface along a path.
Strangely, when the sweep path was well outside of the surface holding the projected curve, the flange was auto-created as I subconscioiusly hoped. When I swept the web, it originated at the rail sweep path's origin, not on the inside face of the surface.
So, using the Gripper, I moved the negative side control point inboard, and at a certain point, the web auto relimited and, now, ALL seems well. (Not counting the desire to have one T be the master for all on its level.)
This is a major leap forward.
The upper anndd lower upright "T" stiffener are what I originally started with.
I used to create a "stick" stiffener, then one-rail-sweep to object the curve, and then thicken that swept surface. But, sometimes, doing things to solids, such as triming them or relimiting in some weird ways takes away the ability to edit the thicknesses in the Inspector, tho it would be possible to use the thicken tool to re-limit the thickness.
But, using a profile with two lines for the web and two lines for the flange means I can adjust thickness by rescaling, or by sliding the web and flange control points up, down, left, or right, and do it with multiple stiffeners if I orient and view-filter the model conveniently.
The middle, inverted T is the actual stiffener profile orientation.
Not apparently visible is the fact that there are two webs and two flanges. The superimposing w & f are there to satisfy me that the profile's shape would remain true once swept from the port-side surface.
Looking at the second photo, you can imagine my satisfaction with this approach because even though I move the control points of the starboard (original surface, basis for the mirrored, port side surface), the curves on (I did not "embed" them "in", just projected onto) the surface automatically/associatively reposition.
If you're designing yachts, dinghys, skiffs, pontoons, or other craft, this might be really useful to you.
What would be really nice would be to drag/copy downward the red profile (inverted "T") and create new, associative, self-limiting beams without having to make all-new web/flange surfaces that would need to be created repetitively.
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