Couple of pieces of advice for you below:
1. the Careers at sea people are really very helpful and give some great advise on their website for the job search. in particaular I found their advise on keeping a job log really good as it gave me purpose and fell like i was getting somewhere. also you can email them your cv and cover letter and they will help you phrase them properly.
2. i wouldn't put to much pressure on the whole thing. I just kept thinking the whole time how much better of I was than everyone else who went to uni. All freshly qualified people struggle to find work at first due to that you need experience to get experience thing ... but at least your not in like 60 grand of dept
3. Try yachts. my first two jobs where yachts , great experience and it gave me that "6-month expeince" . plus a lot of people love them lots of my friends have moved over to yachting. they weren't really my kind of thing but meant i could get a job on cruise ships soo
4. PHONE people. i absolutely hate calling recruiters but it really is the only thing that works.
5. focus on good cover letters. the most honest and frank cover letters i wrote where the ones i got the most replies from.
I think things are bad out there at the moment but they are everywhere (like my mates who are grads cant even get jobs in local shops!). In my option engineers are in a better position that most people out there. so just think positively all the people in my class have got jobs
i wanted to go offshore too but now i have a good job with on a cruise ship which i like so yeah
just focus on getting your orals done jobs will come later
hope that helps (sorry for bad spelling)