LAMWILA,
Unfortunately, the hours, offshore etc., requirements are dictated by the oil companies and there is also the requirement by the Nigerian aviation authorities for an expatriate who works here to hold, or get within a short time of arriving here, an ATPL(H). It's understandable because, naturally they want companies like Bristow and CHC to pay to train more Nigerian pilots. Even in UK some years back, when there was a shortage, not only did Bristow have an ab-initio training scheme, but the Air Transport and travel Industries Training Board subsidised the training costs for a number of helicopter pilots for all the Noth Sea companies, though Bristow did most of the training. In Nigeria now, both companies are paying to send Nigerian pilots for helicopter training overseas.
You'll probably find that when you've got about the hours you mention (2,000 hours TT, 500 turbine) and an ATPL(H), you'll be able to get out to Nigeria. You can probably get away with less than this with Bristow if you can get taken on to fly for their Pan African subsidiary in Nigeria, as they operate mostly Bell 206 and 407s. CHC also sometimes hire on pilots and then then send them to fly for Helijet in Vancouver for 9 months or a year to build up experience and S76 time, but not sure if they do this for pilots who are not either Canadian or American.
Don't give up, as it looks as if you're getting closer to your goals. Good luck.