I bought a twist grip throttle assembly and I had the opposite problem. I made stops to the cable movement to be sure it would not put undue stress on the carb linkage. In addition I added a spring linkage to the final connection to the stupid plastic part on the carb throttle butterfly valve, so when it goes to min or max throttle the spring just bends a minute amount and the plastic does not bend.
Where does this leave you with just the opposite problem? There is a fix, because when making all the linkages with big return spring for the twist grip throttle I had to figure in the amount of total cable movement and match that to the amount the throttle on which the carb butterfly valve could move. The hinge for a door I cut up and used with return spring and that worked for me. I added a length of metal to extend out the movement range of this hinge piece. Then with another stationary piece of metal that the end of the throttle cable came though, I tried various distances from the axle on the hinge metal extension to try and see how much movement I would get. When closer to the axle then more movement with the same range the twist grip has. When further out from the axle less movement with the same range the twist grip has. I will try to get a picture for you to see, but note eventually this will have to be encased with a metal cover to protect it which I will be making as well. The size of this all seems a bit large and a more compact design could obviously been made, so I encourage you to do a little looking around.
But remember the important here is that the angular movement is what makes this adjustable to match the carb butterfly valve range of movement with any twist grip throttle.
One more thing to note is that I had some much movement to the throttle of this twist grip that my wrist could not go that far around to get to go full throttle and that is why I put a stop for maybe around 80 degrees of a full 360 degrees rotation.
What I built works, but it is just the way I did it. If you can find what the manufacturer has to add to the problem you encountered I would start there first. I only had this way of making my setup since the carb that I got was to work on a lawn mower engine and the engine I had even though it was from a lawn mower had a different type of carb so all new linkages had to either be bought or made by myself. I looked at the stuff that was at the go-cart/mini-bike/atv store and nothing would work with my setup.
See in the attached picture where just to the left of my index finger is a hex nut for which a screw fastens that "J" shaped piece of metal to which a powerful return spring is attached. Now just below the hex nut not shown is a fine drilled hole for which the end of the throttle cable goes through and one of those cable stop barrels that has a set screw to clamp down on the cable. Then for where the cable comes from with the sheath stop, look just above that to the stationary piece of metal that has the knurled cylinder with threads and a hex nut holding it in place. The starter recoil pull is a bit close to all this and so a rigid cover I will make to prevent the cord from snapping back and hitting the throttle workings I made.
The black plastic, is butterfly valve on the carb and so it does not get stressed there is a connection to it with a spring underneath the rectangular block of metal. That spring’s hollow center is on a vertical screw attached to the plastic butterfly valve part on the carb. The stops are the other long threaded screws for idle and full throttle stops. When the transfer of the rotational movement from the hinge goes to either stops end, the fine spring underneath I described but you cannot see in the picture, bends slightly, insuring that the full movement for idle min and full throttle max is attained.
Measure Twice