There seems to be alot of confusion here (and I may be adding to it), as chopperpaul just stated, by adding lower resistance bulds (LED, Halogen) will cause the lihts to blink faster and a voltage regulator is needed. That being said, it sounds like to me that when you added a incondesint light to the system, there was too much of a drop for the flasher to work properly and would come steady on.
The comment of removing the indicator light from the dash is cause it dosen't work on a power / ground basis like the other three. It takes power from one side and grounds on the other (example, you turn on the left turn signals and the dash light will ground on the right turn system, and vise versa) which is why you can't install a LED dash light cause it would only work in one direction cause they are polarity sesitive (some modifications with a couple of diodes will fix this though). So in this case, once the turn signals are altered, it'll change the system dynamics and the dash light could work as a link between each side and cause a 4-way flashing effect.
These might some of the issues you are having or not, but hopefullt it'll help you understand the problem a bit more to fixing it.
