Depending upon what lenses you are using with a small-bodied camera with stills-camera lens mounts, you have just about everything conspiring against you when adding a powered follow-focus.
Follow-focus motors tend to be powerful brutes. They have to be.
Simple spur gears attempt to force themselves apart. Ideally they and their shafts/bearings should be in a common rigid housing. That is one rule the typical swing-arm follow-focus breaks with several possible joints in the common structure, the camera to baseplate fixture, the lens to camera fixture, the support rods to camera fixture, the internal mechanism of the lens itself, the integrity of the swingarm of the follow focus throw, flex of the rods, the camera body itself and the lens body, it is something of a minor miracle a geared follow-focus works at all
Simple spur gears are mostly wider in diameter than the shafts they drive. Loading by the friction of shaft bearings against the gears driving them around is relatively low or they just would not be efficient. Most lenses break that rule in that the diameter of the bearing surface of their driven gear (the focus ring itself) is almost as wide as the driven gear. So pressure increases a friction load. The gears under load tend to add a separating force which in turn adds to the friction, a perfect storm and sometimes a cascade to failure when the gears force themselves apart and hop teeth.
So let's look at those points of fixture.
A full cage attached top and bottom to the camera body will help. A half cage may depend too much upon the firmness of the camera base to baseplate attachment. If there is no rubber, the camera will try to twist off its mounting screw unless the screw is very firmly tightened which may distort the camera body itself. If there is rubber on the base faces, then the joint may flex.
Rods into cage/baseplate. - How tight is the fit in the holes and how firmly are they are clamped in place? Some arrangements are better than others but most hollow rods will flex in the holes and along their length.
The attachment of the follow focus assembly onto rods. - By necessity, the contact area of the attachment must be narrow compared to the rods into the baseplate. If the fit to the rods is loose and requires a lot of tightening, then flex will inevitably occur there. Some follow focus motors attach to a single rod and their swing to engage the driven gear on the lens happens on the rod itself a wear point where clearance can open up.
The "offer-twist to lock" lens mount. - Nikon F-Mount, Canon EF-Mount, M43-Mount? These commonly maintain flange face firm contact by the use of a thin spring within the mount ring that the bayonet lugs of the lens tail engage against. Some non-genuine mounts do not use the springs but have built-in compliant faces the lugs engage against which function identically. These are often crudely achieved by slot cuts in the base material of the mount ring.
Why do it this way? Most bayonet-style stills-camera lens mounts also use a locking pin to stop the lens from twisting in the mount and falling out during focus movements. The lens must therefore rotate in the mount a fixed distance to allow the pin to engage. The spring arrangement allows for minute variations in machining of the lens tails, the inevitability of wear on the bayonet surfaces and to a much lesser extent the flange faces.
The rejection forces from a follow focus gear set tend to bend the lens body off-axis, especially if the lens focus system is damped with a high friction lube for smoothness and to maintain working tolerances by filling in the gaps. A point of yield will be the circular spring inside the lens mount which will cause the image to move as one side of the flange face opens up.
The PL-Mount eliminates this problem at expense of not having a locking pin on the twist ring but relies entirely on the fixed pin engagement with a matching slot in the lens tail, which is why you do not transport cameras with lenses mounted if you have any common sense. The Canon FP-Mount was a similar arrangement as are the B4-Mount and B3-Mount. The EF-Mount was really an evolutionary step backwards possibly driven by manufacturing cost.
There have been emulations of this system with alternative Canon EF-Mounts and Nikon F-Mounts offered. P+S Technik with its IMS system and I think RED Corp have had a go at positive lock mounts for Canon and Nikon bayonet style lens tails.
Some modern self-powered stills-camera lenses with plastic bodies eliminate damping frictions due the necessity to get the most out of the limited power available from internal servomotors. Simply allowing more generous clearances and an optional disconnect of the focus ring from the focus system when autofocus is selected introduces the possibility of image shifts when focus trims are made. Wear and age will weary them and make the issue worse for motion video work.
There is not much to be done about a sloppy lens except to buy something else.
The traditional externally mounted geared follow-focus is really just a workaround which became an industry standard and was eventually powered. ENG servo lenses were a far more elegant solution, some better than others.
So after all that barely scientific fluff and crappenstance discourse, what to do?
A full cage with upper and lower fixture for the camera will be helpful. A decent baseplate with snug fit around rods and cam levers versus split clamping is desirable.
Solid rather than hollow metal rods will be helpful to avoid torque bending of the rods.
A good solid bridgeplate and chair under the front of the lens plus a secure strap or even a saddle clamp across the front will be very helpful to resist torque bending. It will be absolutely useless if the lens body does not have internal focusing. Even a ziptie across to the rod most opposite the driving gear will be helpful but all this will make lens changes a pain in the ring.
Mike Patey of Best Tugs in the US has developed and vends reusable zip ties apparently to aviation standards.
https://www.besttugs.com/A good solid bridgeplate will be assisted by a mattebox with its own good solid bridge to further firm up the rods against bending.
So what about the corrugated spring inside the Canon EF-Mount and Nikon F-Mount? There is not much to be done as the fit is precise. You might be able to increase spring tension slightly by adding small shims under the spring but making those will be extremely complicated and frankly not worth the effort. - I have tried.
Compliance within the camera body itself from forces occurring between the lens mount and camera base. A full cage will spread the perimeter loading on the camera body but will not address concentrated loads occurring at the lens mount. Given the non-modular nature of the electronics layout, any compliance within the camera body is not ideal as it will work electrical joints which are a known weakness in modern leadless surface-mounted PCB designs.
The more you can stabilise the mechanical bond between the lens body and the rods/baseplate the better.
Now we run into the final dilemma. How long is a piece of string. You may build a tank of a setup, then do hour back in with the struggle and grunt of carting it about and get it caught in hedges or snag long flowing hair. (Note my political correctness in avoiding sexism). When the person grabs a hank of that long flowing hair to haul it free, you are fated to be pulled off your shot.
My first step would be to make a bridgeplate, chair and saddle for the front of the lens and incrementally build from there. The bridgeplate should be easy to get hold of but don't stuff around with those halfcircle clamp-ons or the cheap split circle and draw rods versions. For torsional strength both types are ornamental but poor in firmness.
The chair and saddle may have to be 3D printed or custom machined for the front of your lens.
Meanwhile, you can try a strong zip tie around the front of the lens body down to the rod most opposite the drive-gear-driven gear contact point and cut a piece of thick plywood to work as a triangular wedge with hooks between the rods and a chair to match the bottom of the lens front. Be careful not to tension it down too much or you may break the camera or pull it around on its baseplate.