What Agencies Should I Contact?

I read comments from people that said the economic situation for new teachers in Taiwan was dire. I am an experienced teacher, who spent over a year in Japan and some time in Korea. Last year I was considering Taiwan. I contacted De Wey and was amazed at their prompt-same day- reply. Sadly, I had to stay in the U.K. but informed the agency quickly. This year I contacted them (AND OTHERS) again. No reply in one week. Are there any agencies that are worth contacting? Could they find me a job in a major city?
I realise I am not eligible to teach in public schools there. It does seem unfair to be limited to just private schools, but this could change in the long term if another government came into power.

A list here: List of Agencies and what you should know about them