Spike, I don't think that lower power bulbs will make the signals flash quicker, in fact they should do just the opposite and make them flash slower. The common automotive flasher unit uses a bimetalic contact that bends as it heats up and opens the circuit then straightens as it cools and re connects. The lower the current in the system the slower it flashes because it heats up slower. That's why when you have an burned out bulb on most systems you don't get a flash on that side, not enough current through one bulb to heat up the element. Check with superbrightleds and see what type of flasher they recommend, you might have to upgrade to a solid state flasher unit to get things working.
As for the original problem, I realize that the headlights take a lot of current, but I suspect that you have a poor connection somewhere in the system that is dropping your voltage with the headlights on and causing the slow or non flash. A good battery should be more than able to supply enough amperage at 12v to run both the headlights and flashers, it uses many times more current to run the starter. I think that if you sort out the resistance problem either in the power side or ground you will be more than pleased with the illumination from the signals.
'73 Midget (V6)
'59 MGA (I6) under construction
'73 Lotus Europa
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