A320 I don't think the 1000-2000hrs is actually a problem in the UK. There were quite a few instructors out there with those hours, the average is dropping quite quickly.
If you put the work in, network and all that other good stuff you will have as good chance as anyone else. Aussies and Kiwi's have quite a good reputation the UK. If you have reasonable IFR time you might be pretty useful for a single crew air taxi operator.
You don't want to get into the trap of being seen as a shiny jet wannabie. In my opinion nothing more likely to put off TP operators than seeing a MCC on a 737 sim.
I would be prepared to take almost any job as my initial one in the UK/Europe, but I am starting to get the impression that I would need to pay for a type rating in addition the license conversion to have any chance of employment with a European airline????
The first statement says to me that you would proberly succeed. The second statement is untrue. In fact if you go for the wrong rating in can cause you more problems than it solves as A320 has found out.