Using an eyedropper and trial & error/intuition/experience will probably work fine. Here is a fishless cycling calculator I wrote a while ago. It assumes the percentage of Ammonia solution is using the mass/volume standard, which is not always true. (I am fairly sure Flourish and know Tropica use mass/mass, for example.) So, you should test with a control first, then guestimate the ammonia production of the removed fish.

(If using a non-compliant browser, submitting info will redirect to the top of the page, and you can click on "general solutions" to jump to the result. Relevant links for the calculation are below the formula.)

A bigger holding tank for the Comets would probably help a lot with survival, and it's likely there's simply too much of a bioload in the 10g to maintain stability. I think your problems could be alleviated with a big holding tank, like a 50gal (fish-safe) trashcan. But you surely know this already

Just more thoughts. If the feeders get sick or weak, does it affect aquatic snakes?