I don't know if you're looking for advice, and if you're not, read no further. However, if you are looking for a little something in the way of a rejoinder...

...it seems that you have the sensitivity and perspicacity to realise when things aren't going well and, furthermore, it concerns you when things aren't going well. Now prepare yourself for a shock my son. These are not traits commonly to be found amongst those of the general population, never mind among the many employed as English teachers in China or anywhere else for that matter.

You could either:
1. Give up.

2. Keep going and try meditation or alcohol as a means to suppress the guilt.

3. Keep looking for a better way to do things and eventually get good at what you do(with the result that you would eventually be able to do your job successfully with less prep, much less anxiety, and for more money).

A class such as you describe would really give you a great opportunity to experiment. Let's face it, it sounds like things couldn't really get any worse in there at the moment!

Some suggestions for choice 3 above:

1. Relax.

2. Keep looking for a better way and realise that you have to pitch at both those you consider as your "best" and those you consider as your "worst" performing students (you might be surprised as to where abilities actually lie).

3. Know when it's time to stop trying with students who don't want to do anthing, and focus on those who do.

4. Be suspicious that there might be more to teaching than just presenting a continuous succession of those often ridiculous activities as taught by allegedly prestigious teacher training outfits. ie students do appreciate being taught something now and then. Find something concrete to focus on occasionally.

5. Find out what others are doing to make their classes so allegedly fantastic and brilliant, and - if there's anything worthwhile - use it or adapt it.

6. Realise the fact that you do care probably means that you're doing better than what you give yourself credit for.

7. Don't be afraid to try new things.

8. Don't be worried about just spending time on simple things like reading aloud to them, getting them to read aloud (thereby checking their pronunciation, voice modulation, phrasing, comprehension, vocab etc etc) or engaging them in simple discussions about things that interest them or are of direct relevance to them. Even making an effort to find out about such things has the effect of lessening the social distance between you and your students, allows you to understand them better, and selfishly allows you angles from which to approach future lessons.

9. Encourage students to help each other. Use your more advanced students to help the slower ones; encourage them to explain to each other (in any language) what is it is you as the teacher are expecting them to do. Get students to check each others work and to be critical of each others language usage and of yours.

10.Your aim is not to be knocking yourelf out. You present and direct. They do the work. Any materials preparation that could be done by students should be done by students at your direction.

11. Ignore this "Joe". As a recruiter or agent he obviously has his best interests at heart;

12. Relax.

13. etc...

I agree with you that the sentiments you describe are underepresented in everyday conversation or on internet fora. Very rarely do you come across such an admission as yours. It's a matter of honour; nobody wants to admit that they don't know what they're doing, and let's face it, in this world there aren't many who really do know what they're doing.

I certainly don't.

(Sorry if all this was uncalled and or for any offence caused.)