Horn switch turns starter motor over?!

I promise to post some pics of the project that is now nearly 3 years long, however I'm stuck on an odd issue as follows;

Pressing the horn button kicks the starter and turns the engine over but only with replacement horns I've tried (I've tested 3 so far) plug the original horn back in and it works as a horn and doesn't turn the starter over...

For some background - this is an '82 KZ750H which I have cafe racer'd. Existing loom but heavily adapted as follows;

LED indicators and solid state indicator relay
New handlebar switches (online specials but other than the horn all working)
MotoGadget RFID ignition switch (no keyed ignition)
Digital Speedo
Removal of Failover light function

The wiring diagram does show that the starter and horn share a common 12V supply, so I guess there's been a mistake that allows the horn button to provide power to the starter solenoid. Just very odd that this doesn't happen with the OE horn?!

Any insight appreciated!

Thanks

Based on your description and my very limited understanding of electricity, I'd say that the aftermarket horn needs significantly more power than the stock horn. Also, do both the horn and the starter buttons have good, clean ground to the handlebar? A painted bar can be a real problem. If the horn does need more power, you may need to wire a relay to the button that can supply sufficient juice to the new horn.
Somebody who knows better than I will be along shortly to sort us both out.