Bicycle mechanics often fix this problem by removing some of the housing to shorten it without having to replace the inner cable. Cut off as little of the inner cable as you can to remove any fray, maybe a half inch, pull the cable a few inches through the housing, and see if you can cut an inch or so off the housing and still have it reach the bracket. Then the amount of cable revealed may be enough to crimp on the eye end.
Anyone consider crimping the cable to an adjoining cable?
The barrel adjuster for a bicycle looks like this, similar to a throttle cable setup if you use two nuts on it. This would replace the white plastic end on the housing and make the whole thing adjustable to take out any slack.
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