Just flushing with the components in the shutter will not get the gunk out. You have to remove every thing, flush, lube, reassemble.
A light sheen of oil is all that is needed, any more acts like glue.
Light weight grease is better on the gear teeth, again just a trace.
The main plate needs to be removed, the shutter blades and controller removed from the plate, cleaned, and lubed with an extra fine dry powder lubricant such as extra fine powdered graphite.
Adjust the 1 second or the lowest shutter speed for correct for the best chance of other speeds being correct. Older spring tension shutters can be improved by increasing the springs tension, if the spring arms are at 45° to each other uninstalled increase the angle to 50° to 55° without distorting the springs center. Extension springs can have 1 to 3 turns removed and the end reformed to the attach end shape.
Speeds above 1/100 - 1/125 use booster springs to achieve the speed, sounds like yours is good.
Speeds 1/100 and slower are 20% tolerance, Speeds 1/125 and faster are 30% tolerance or roughly 1/3 stop either side of the marked speed.