That's a shame about the recruitment companies. Even though I recommend persevering with them, I do have a few suggestions . However, sometimes a proactive search can be the most rewarding.
With this in mind, you should explore some of the job portals for the Gulf and Middle East. Sites like this include Akhtaboot, Bayt, Dubizzle and Gulf Talent. Social media has become quite a useful way in trawling the job market in Abu Dhabi and abroad.
Do you have a LinkedIn account? By stating your previous job experience, internships and positions, you can perhaps entice recruiters and companies to contact you. I myself have received job offers from Dubai on the site. If you build a strong profile, it may increase your chances of receiving an offer.
Prospective employers also use organisations on this platform to post listings and vacancies. WIth a quick search, they won't be too hard to find.
Lastly, many expats who move to the Abu Dhabi and the surrounding regions are often part of international companies. These companies have affiliated branches where they can send you. By researching a little, you could find a few and contact them directly with employment inquiries.
If you do crack the position, make sure you have the appropriate work permits before making the trip. The employers should help you out with most of the paperwork and bureaucratic hurdles.
Hope this helps a little!