First off, more time on the water will help in figuring things out. Quit "throwing the rod at the fish" (too much upper arm) Now, if I'm getting the jist of this "swing weight" meaning the weight felt during the cast, as opposed to the weight felt holding the rod for the duration of the swing? And being set up for Skagit casting, would it be safe to assume sustained anchor (water born) casts?
So here we go, my humble opinion (often a wee bit more opinionated
) along with the disclaimer, I am totally clueless of the characteristics of your rod. That being said, a 600gr Skagit Flight head coupled to 10ft of T-10 does not seem out of line for a 13'-6" 8wt rod. T-14 would depend on the tip diameter of that Skagit Flight head. (.080 minimum for good turn over)
Until you get used to it, it will feel heavy lifting a sunk tip to the surface, no matter what rod reel you are using. After the lift & the setting of the anchor, the cast begins with the sweep. If
and this is a big if, done properly (& that alone is subjective) the sweep need not be physically assertive, as long as you maintain constant tension on the line! When everything is lined up & you pull the trigger, do it with the bottom hand. You need not hold a death grip on the rod for any of the SA casts. Only momentarily, on the hard stop do you need to tighten up on the grip. Like anything else, it's all in the timing.
Like said there is a difference in the feel of a tip action rod & those flexing deeper into the blank. There is also the weight & position of the reel, reel seat up or down locking & the length of the corks. These are just the laws of physics, mostly involving E=MV² & lever arms. Velocity squared having more effect than mass, rod weight is of little concern here. The lever arms being rod length (subject to change with deflection) and hand position from the reel.
Personally, I like heavy reels, up locking reel seats & full flexing rods with adequate length corks. And I line them with enough grains to load all the way down into the corks. YMMV