Did my conversion from Cdn ATPL to UK ATPL. Completed 2002. Found work in 2003 flying heavies. Had 3000hrs when finished conversion, and many positive responses from operators in the UK. Had my sights set on one place in particular though, and lucky for me it worked out. Lack of jet experience is not a big problem. 3000hrs is considered pretty decent time when many of the jet operators will hire f/o's with 500hrs tt.
Know 4 others from Canada who did the same thing. We're all working for large international airlines flying widebodies, so I'd say it worked out pretty decently. I believe we all had between 2000-4000hrs when we finished our conversions. Keep in mind all of us also have UK (dual) citizenship, and would all rather be living in Canada, but the opportunities are simply better in Europe. You MUST have an EU passport to make the JAR license worthwhile though.