Gotcha - yep, even simple circuitry can become really confusing shit. I remember the electron flow being opposite conventional circuit flow throwing me for a loop back in school - one reason I stuck with nuts & bolts!
As you pointed out, the circuit was designed for incandescent bulbs which draw more current & thus cause more voltage drop - so the indicator diodes 'see' less voltage normally. I'm thinking that the higher voltage present on the indicator circuit due to lower drop across the LED's is a bit above the 'breakdown voltage' (point at which the diodes quit blocking) - so there's the 'leakage' to the opposite signals.
Trick is, figuring out how much additional resistance is required in the circuit to drop that voltage below the threshhold.