welcome to the forum, Matt.
your carbs should come off for a chem dip and then a thorough, and i mean
thorough, cleaning with carb cleaner/simple green.
the MC can be cleaned with brake cleaner. lines flushed, and refilled with new brake fluid.
But dont clean just the MC. you'll need to service the caliper, too, by removing the piston, and at a minimum, replacing the piston seal. if there's gunk in your MC, there's gunk in the caliper, which is not a good thing, especially if you want to, you know...STOP