Work /
Companies within Poznan (positions available for native English speakers) [18]
There are very few companies that will hire native English speakers who aren't competent in the Polish language. The ones that do hire are the ones that are either (as you've already found out) call centres, or they're looking for people with skills that far exceed what you have.
Put it this way - what do you offer that the average Polish graduate doesn't have? I've just posted a job advert yesterday for a PA - with fluent English being required. So far, I've got over 50 CV's to look through - in less than 24 hours. You're immediately at a disadvantage compared to them - and they all have degrees. There's even more and more non-EU citizens with reasonable skills in Polish looking for work, too.
I know someone that might be interested in hiring you on a commission-only basis, but that's about it. Could be good money, could be crap - hard to say. It's still a job, I suppose. If you're interested, let me know.
If you couldn't hack it in the airlines call centre and couldn't get enough work as a teacher - have you thought about calling it a day? There really aren't many more businesses willing to hire someone who only speaks English.