Billy,
I must confess that your post leaves me somewhat concerned. As a retired licensed engineer (mainly GA), my last employer was a Part-145 organisation responsible for maintenance on several examples of the 2002, although I was never personally very involved in its maintenance and can't speak from direct experience. Our Tecnams were not highly regarded by my colleagues, particularly in terms of build-quality (which should not affect your example), but I believe it is well designed to conventional airworthiness criteria. I am surprise by your absence of rigging data, either in the form of a maintenance manual or assembly process sheets. You have a kit, but no instructions? Some points to consider;
1. Almost no aeroplane has its flying control range-of-movement determined by how far you can move the stick. Each aileron should have "primary" stop, in the form of an adjustable-length bolt, normally acting on each aileron's input bellcrank, and limiting the movement of the aileron (whether it is attached to the rest of the control-system or not).
2. There should be a "secondary" stop adjacent to the control stick. The purpose of the secondary stop is, on a completely rigged system, to limit the amount of tension/compression that can be applied to the system when the ailerons are at full travel, to prevent overstressing the control system. When the stick is moved gently to the limits of travel (ie, when the primary-stops make contact) there should be a small gap at the secondary stops, which can be closed by further pressure on the stick.
3. The system must always be rigged initially with all its contituent parts in "neutral". There should be a means of securing the stick in neutral, perhaps a rigging pin or clamp. The ailerons should normally be placed in neutral by aligning with the T/E of the wing. This is important; the bellcranks should also be secured in neutral. It is not sufficient that the stick-and-aileron are neutral if the bellcranks are at weird angles, as this will give a non-linear nmovement of the aileron in response to movement of the stick.
4. With all the components in neutral, prepare the pushrods by screwing each rose bearing in equally. Install the pushrods by adjusting the rose bearings equally until the attachment bolts slide in freely. There should be a defined means of ensuring that the rose-bearings have sufficient threads engaged.
5. Install the cables and turnbuckles, tighten the turnbuckles to take up the slack whilst ensuring that the stick and bellcranks remain in neutral. Tighten the turnbuckles further (equally) to achieve the specified tension.
6. Remove all your rigging pins and clamps. Ensure that the controls move freely, in the appropriate direction, and to the correct range.
7. Absolutely vital;
a. make sure that you've removed all your tooling.
b. make sure that the controls move in the right direction.
c. make sure that all threads are sufficiently engaged.
d. make sure that all locking devices/safety-wire are installed and secure.
e. make sure that a competent person performs a duplicate inspection of b. to d.
f. check again that the controls movie in the right direction!
8. Although you've only asked about an aileron problem, everything applies to the other control systems as well.