The key is patience! The
patina took centuries to form and your coins were covered in dirt for thousands of years. so don't expect a quick fix if you want to do it properly. (For me, the most difficult
part was learning to wait and knowing when to stop.)
I agree that there isn't much benefit to cleaning the second coin. I'd just wax and
flip it.
Acetone is pretty potent and might be a lot more than you need for the first coin. I haven't used diluted ammonia, but my guess is that it would need to be a pretty short soak before scrubbing with a toothbrush (tissues or papertowels are essentially worthless for anything other than drying) and a distilled water soak before drying. The distilled water will neutralize the ammonia. (Tap water is not recommended since it has a variety of chemicals that can potentially damage your coin, by the way.)
If you want, consider a
good soak in distilled water (several days) followed by a scrub with a toothbrush and/or pin or
dental pick (easier to
handle, in my opinion). Repeat if you think it's necessary. Then, if you are
still unsure of the results you can go with short soaks in ammonia or even vinegar or lemon juice.
Post your progress and let us know how it's going.
Best,
Tony