You certainly have an impressive CV which will work in your favour when scouring the online job market. I suggest you visit emplopyment portals for the Middle East and even some local ones like The Guardian. Companies may be looking to hire for their international branches, some of which may be in the Emirates.
Some job portals I suggest would be Gulf Talent, Bayt, Dubizzle, Monster Gulf, Naukri Gulf, Khaleej Times and CareerJet Dubai. For a little background, I'd also take a look at our job market pages on Oman, Qatar, Saudi Arabia and Dubai.
I also suggest you create some type of online portfolio or resume. For this, LinkedIn is by far your best option. On it you will be able to list all your working experience and previous projects. In addition, you will be able to network with others in the market, either like-minded colleagues or keen employers.
Once your profile is up and running, you may even be contacted by interested companies. I myself can attest to this as I was approached by potential employers in Dubai.