A 3-pronged hand tool is good for raking/grabbing bermuda grass off of mulch. Just keep at it. In the rainy season you will need to toss the grass (and bits of clinging mulch) into a bin, but in the summer you can just rip it free from the soil and let it dry out. Instead of chop and drop, sort of rip and drop.
Don't try to do the whole yard, just protect your favored plants. Think of the guys that paint the Golden Gate Bridge - just keep repeating. That grass is pulling carbon from the air, so thank you grass, we just don't want you here.