Sorry to read of your intermittent starter issues and can not recommend any one to effect repairs.
It seems you have an understanding of the basic low current circuit operation which by your description works to the extent that the solenoid mounted on the starter is activated, as indicated by the sound of a clunk but nothing beyond that..?
The solenoid mounted on the starter performs two functions when the low current coil within it is activated, the first of which is to draw a plunger into the now magnetised core of the solenoid. One end of the plunger acts on a lever which then attempts to engage the starter motor gears with the teeth on the flywheel... at the same time the the other end of the same plunger acts on HEAVY electrical contacts, which short out the two heavy wiring terminals terminals on the outside of the solenoid... one of which is the POSITIVEpower lead direct from the battery, the other being connected to to the internal windings of the starter MOTOR, when both are shorted together STARTER MOTOR turns
For this all to happen in the mechanical sense, the teeth in the gearing of the starter motor must match those in the flywheel for them to be able to engage fully. There is usually a chamfer on the leading edge of the teeth to assist engagement... and if for any reason the teeth do not fully engage then the plunger within the solenoid can not complete it`s travel to close the heavy electrical contacts to drive the starter motor... which seems to be the stage of the game you may have reached..?
Of course any dirty/cruddy connection in the high current wiring will provide similar results.
If you have not been able to determine the earth link body to engine/ gearbox assembly as being fully up to the task, then I guess you could use a set of jump leads linked together to provide a direct connection from the battery NEGATIVE terminal with one clamp end, and the other clamp end to a good clean and bare metal part of the engine/gearbox assembly, and then try for a start. The electricity does not care as to the colour of the insulation on the jump leads... just that YOU have to be well aware of what to connect to.. Nothing will be carrying current until you turn the key into the start position.
You could pull the DME relay to avoid the engine actually firing up, and thus then be able try numerous attempts without the engine firing up..? If it turns over numerous times and without issue then you may well have found the cause...?
Should you be tempted to use a bit of wire you have lying around and not of the required current carrying capacity, it could heat up and melt or set fire to the insulation along it`s entire length with who knows what consequences..?
Good luck..Please let us know how you get on.