A diatonic, right? Please don't boil them again!
Put a towel down before you dismantle it (voice of experience here). Otherwise, you'll be chasing bouncing screws, I guarantee.
Once you have it apart, use a soft toothbrush as suggested. You can use something like a dental pick to flick some of the dried gunk off the comb. However, it sounds as though you're going to have to take more drastic measures than these.
Be very careful with the reed plates. Brushing with too much pressure can change reed reed height and you'll get buzzing and dead notes (then you'll be in the reed re-setting business in addition to a deep clean.)
You probably have dried saliva and perhaps food particles (delightful!) on the reed plates. If there is material you can see, one of the best ways to begin is to put the reed plates, the covers and the comb (not if the comb is wood) in water and let it stand 5-10 minutes. (You can add a little bit of white vinegar to this, but if you do, be sure not to let it soak too long and rinse, rinse, rinse once it emerges from its bath.) Remove, rinse and work gently with the soft tooth brush and then dry carefully with a lint free cloth (Microfiber works great). If you still have gunk, you can bring out the big guns: a bit of baking soda and a dash of white vinegar. Make a paste and gently use a toothbrush to try to dislodge leftover gunk. Then keep rinsing these parts with water until the cleaning solution is gone and dry thoroughly.
My Dad played for 70 years and he taught me how to keep them clean.
One Idea that I have not tried (but plan to do) and should work beautifully is to use plain water in a small ultrasonic cleaner. If you play harps on a regular basis (and it sounds like you do), that would be an inexpensive and easy way to keep them cleaner. With this method, you take the harp apart, put let the ultrasonic do its work for 10 minutes or so, remove, brush gently with the toothbrush and completely dry the parts.
I play diatonic and chromatics and it's fun to tinker with them. Good luck.
Bluesy.
