I would guess from your description that changing out motors is not a trivial task. There are things that you can do though. Check the axle driven by the problem motor for mechanical issues. Bad bearings, (Dragging Brakes?) bad gearboxes if fitted etc. If you don't have a spare 1336 VFD, try swapping two of them, and see if the problem stays on the same axle, or moves with the VFD. Bring in your nearest motor shop with better test equipment, and have them do a test of the motor. If the motor can be uncoupled easily from the axle, uncouple it, and spin the motor looking for mechanical problems like bad bearings etc. The shaft should spin freely without any tight spots or bad noises.
You only really have 3 choices, either there is a mechanical problem with the axle causing the overload condition, there is a problem with the motor, or there is a problem with the VFD, which could also include its power and motor wiring, inline inductors etc. For instance, a bad connection on one of the phases to the motor could cause higher current on the remaining two phases.
Since you describe it as a motor overload, in my experience that is almost always a problem in the connected load. The next most common problem is the motor, wiring issues surrounding the VFD, and very rarely, a problem with the VFD (failed internal component etc).
Others may have had different experiences, but that has been my experience working on well over a thousand Motor Systems, and hundreds of VFD/Motor systems.
Stu.....