Hi,
also the fowlerflaps increased the drag, the main different is: The normal flaps have a bad airfoil as result and the part of the wings outside the flaps use a other AOA, as result wings with "normal" flaps dont create much more lift in general, but shift the stallspeed to a lower value. Fowler flaps, specialy in the manouver flap position, increase the wingarea and keep the AoA of the whole wing rather constant, as result the lift realy increase and so more tight turns can be flown, though for the price of a higher E-bleed.
The only way to create more lift, without more drag is to increase the wing aspect ratio(with same wingarea), but even this only count for speeds when mach related problems dont matter.
Otherwise more lift = more drag.
Greetings,
Knegel