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Is this the model ?
I had plenty of problems adjusting it and it still isn't perfect. I'm not sure if you can see it but I bent the end of the plunger spring around so it would tighten up against the carrying arm, because as you said there is no slotted barrel cup to adjust or hold the spring in place properly.
Also ensure to turn the tension arm spring as far you can clockwise before tightening with the pivot locking screw and then pull back spring and hook behind the carrying arm to give maximum tension.
have you read this?
http://www.classiclightweights.co.uk/simplex_adjustment.html
Take it slowly and make sure you are satisfied that each step is completed.
I will message you with the Simplex Fitting Instructions issued by Simplex.